263179874-Pre-Algebra-Homework-Book

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 45 Course 2 3-1 A Determine whether the relationship between the two quantities described in each table is linear. If so, find the constant rate of change. If not, explain your reasoning. 1. Fabric Needed for Costumes Number of Costumes 2468 Fabric (yd) 7 14 21 28 2. Distance Traveled on Bike Trip Day 1234 Distance(mi) 21.8 43.6 68.8 90.6 For Exercises 3 and 4, refer to the graphs below. 3. Hawk Diving Toward Prey Altitude (ft.) Time (s) 100 80 60 40 20 0 2 4 6 8 10 Y Z a. Find the constant rate of change and interpret its meaning. b. Determine whether a proportional linear relationship exists between the two quantities shown in the graph. Explain your reasoning. 4. Book Sales Sales ($) Day 5,000 4,000 3,000 2,000 1,000 0 2 4 6 8 10 Y Z a. Find the constant rate of change and interpret its meaning. b. Determine whether a proportional linear relationship exists between the two quantities shown in the graph. Explain your reasoning. Get Connected Get Connected For more examples, go to glencoe.com. Homework Practice Constant Rate of Change 045_060_HPC3C3_892764.indd 45 45_060_HPC3C3_892764.indd 45 2/2/10 11:51:14 PM /2/10 11:51:14 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 46 Course 2 3-1 A FLOWERS For Exercises 1 and 2, use the graph that shows the depth of the water in a vase of flowers over 8 days. LONG DISTANCE For Exercises 3–6, use the graph that compares the costs of long distance phone calls with three different companies. 1. Find the rate of change for the line. 2. Interpret the difference between depth in inches and the day as a rate of change. 3. Interpret the difference between the cost in dollars and the length in minutes for Company A as a rate of change. 4. Interpret the difference between the cost in dollars and the length in minutes for Company B as a rate of change. 5. Interpret the difference between the cost in dollars and the length in minutes for Company C as a rate of change. 6. Which company charges the least for each additional minute? Explain your reasoning. y x 0 1 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 Depth of Water in Vase Depth (in.) Day y x 0 123456789 0.50 1.00 1.50 2.00 2.50 Long Distance Charges Cost ($) Length of Call (minutes) Company A Company B Company C Problem-Solving Practice Constant Rate of Change 045_060_HPC3C3_892764.indd 46 45_060_HPC3C3_892764.indd 46 2/2/10 9:57:27 PM /2/10 9:57:27 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 47 Course 2 3-1 Find the slope of each line. 1. y O x 2. y O x 3. y O x The points given in each table lie on a line. Find the slope of the line. Then graph the line. 4. x -1 135 y -2 024 5. x -2 3 8 13 y -2 -1 0 1 6. x -1 258 y 3 -1 -5 9 y O x y x 4 8 12 16 8 4 4 8 O y -8 48 -4 x 8 4 4 O - -8 7. HOMES Find the slope of the roof 8. MOUNTAINS Find the slope of a of a home that rises 8 feet for every mountain that descends 100 meters for horizontal change of 24 feet. every horizontal distance of 1,000 meters. 24 ft 8 ft 1,000 m 100 m Find the slope of the line that passes through each pair of points. 9. A(1, 3), B(4, 7) 10. C(3, 5), D(2, 6) 11. E(4, 0), F(5, 5) 12. P(-2, -5), R(2, 3) 13. S(-7, 4), T(5, 2) 14. V(9, -1), W(7, 6) 15. SNOWFALL Use the graph at the right. It shows the depth in feet of snow after each two-hour period during a snowstorm. a. Find the slope of the line. b. Does the graph show a constant rate of change? Explain. c. If the graph is extended to the right, could you expect the slope to remain constant? Explain. Depth (ft) 2 1 0 3 2 8 12 4 6 10 Hours y x Snowfall Get Connected Get Connected For more examples, go to glencoe.com. C Homework Practice Slope 045_060_HPC3C3_892764.indd 47 45_060_HPC3C3_892764.indd 47 2/2/10 9:57:33 PM /2/10 9:57:33 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 48 Course 2 3-1 1. MOVIES By the end of its first week, a movie had grossed $2.3 million. By the end of its sixth week, it had grossed $6.8 million. Graph the data with the week on the horizontal axis and the revenue on the vertical axis, and draw a line through the points. Then find and interpret the slope of the line. 0 2 4 6 8 10 2 4 6 8 10 Revenue (millions of dollars) Week 2. BASKETBALL After Game 1, Felicia had scored 14 points. After Game 5, she had scored a total of 82 points for the season. After Game 10, she had scored 129 points. Graph the data with the game number on the horizontal axis and the number of points on the vertical axis. Connect the points using two different line segments. 0 2 4 6 8 10 40 80 120 160 Number of Points Game 3. BASKETBALL Find the slope of each line segment in your graph from Exercise 2 and interpret it. Which part of the graph shows the greater rate of change? Explain. 4. GEOMETRY The figure shows triangle ABC plotted on a coordinate system. Explain how to find the slope of the line through points A and B. Then find the slope. y O x $(2, -2) #(2, 4) "(-3, -2) 5. Use the figure in Exercise 4. What is the slope of the line through points A and C? How do you know? 6. Use the figure in Exercise 4. What is the slope of the line through points B and C? How do you know? C Problem-Solving Practice Slope 045_060_HPC3C3_892764.indd 48 45_060_HPC3C3_892764.indd 48 2/2/10 11:51:39 PM /2/10 11:51:39 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 49 Course 2 3-1 Get Connected Get Connected For more examples, go to glencoe.com. 1. ADVERTISING The number of vehicles a dealership sells is directly proportional to the money spent on advertising. How many vehicles does the dealership sell for each $1,000 spent on advertising? 2. SNOWMOBILES Bruce rents snowmobiles to tourists. He charges $135 for 4 hours and $202.50 for 6 hours. What is the hourly rate Bruce charges to rent a snowmobile? 3. SOLAR ENERGY The power absorbed by a solar panel varies directly with its area. If an 8 square meter panel absorbs 8,160 watts of power, how much power does a 12 square meter solar panel absorb? 4. INSECT CONTROL Mr. Malone used 40 pounds of insecticide to cover 1,760 square feet of lawn and 60 pounds to cover an additional 2,640 square feet. How many pounds of insecticide would Mr. Malone need to cover his whole lawn of 4,480 square feet? Determine whether each linear function is a direct variation. If so, state the constant of variation. 5. Volume, x 2468 Mass, y 10 20 30 40 6. Gallons, x 5 10 15 20 Miles, y 95 190 285 380 7. Time, x 8 9 10 11 Temp, y 68 71 74 77 8. Age, x 3 6 9 12 Height, y 28 40 52 64 ALGEBRA If y varies directly with x, write an equation for the direct variation. Then find each value. 9. If y = -5 when x = 2, find y when x = 8. 10. Find y when x = 1, if y = 3 when x = 2. 11. If y = -7 when x = -21, what is the value of x when y = 9? 12. Find x when y = 18, if y = 5 when x = 4. Vehicles Sold 40 20 0 60 80 2 8 12 4 6 10 Advertising ($1,000's) y x Dealership Sales E Homework Practice Direct Variation 045_060_HPC3C3_892764.indd 49 45_060_HPC3C3_892764.indd 49 2/2/10 9:57:47 PM /2/10 9:57:47 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 50 Course 2 3-1 1. JOBS The amount Candice earns is directly proportional to the number of magazines she sells. How much does Candice earn for each magazine sale? y x Earnings ($) 10 5 0 15 20 25 30 35 1234567 Magazines Sold 2. MANUFACTURING The number of cars built varies directly as the number of hours the production line operates. What is the ratio of cars built to hours of production? y x Number of Cars Built 40 20 0 60 80 100 120 140 1234567 Production Hours 3. DRIVING A car drives 283.5 miles in 4.5 hours. Assuming that the distance traveled is directly proportional to the time traveled, how far will the car travel in 7 hours? 4. MEASUREMENT The number of kilograms that an object weighs varies directly as does the number of pounds. If an object that weighs 45 kilograms weighs about 100 pounds, how many kilograms is an object that weighs 70 pounds? 5. RECORDING The amount of cable that is wound on a spool varies directly with the amount of time that passes. Determine the speed at which the cable moves. y x Cable Length (in.) 20 10 0 30 40 50 60 70 1234567 Time (s) 6. GEOMETRY The width of a rectangle varies directly as its length. What is the perimeter of a rectangle that is 15 inches long? 5 in. 12.5 in. E Problem-Solving Practice Direct Variation 045_060_HPC3C3_892764.indd 50 45_060_HPC3C3_892764.indd 50 2/2/10 9:57:52 PM /2/10 9:57:52 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 51 Course 2 A State the slope and the y-intercept for the graph of each equation. 1. y = 4x + 1 2. y = -3x + 5 3. -x + y = 4 4. y = 5 − 6 x - 3 5. y + 3x = -7 6. y = 1 − 5 x + 2 Graph each equation using the slope and the y-intercept. 7. y = -2x + 2 8. y + x = -3 9. 1 = y -2 − 3 x y 0 x y 0 x y 0 x 10. CAMPING The entrance fee to the national park is $15. A campsite fee is $15 per night. The total cost y for a camping trip for x nights can be represented by the equation y = 15x + 15. a. Graph the equation. b. Use the graph to find the total cost for 4 nights. c. Interpret the slope and the y-intercept. 11. GEOMETRY Use the diagram shown. x y x  y  90 a. Write the equation in slope-intercept form. b. Graph the equation. c. Use the graph to find the value of y if x = 30. Get Connected Get Connected For more examples, go to glencoe.com. 3-2 Homework Practice Slope-Intercept Form 045_060_HPC3C3_892764.indd 51 45_060_HPC3C3_892764.indd 51 2/2/10 9:57:57 PM /2/10 9:57:57 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 52 Course 2 A CAR RENTAL For Exercises 1 and 2, use the following information. Ace Car Rentals charges $20 per day plus a $10 service charge to rent one of its compact cars. The total cost can be represented by the equation y = 20x + 10, where x is the number of days and y is the total cost. 1. Graph the equation. What do the slope and y-intercept represent? y x 0 2 4 6 8 10 40 80 120 160 Cost ($) Number of Days 2. Explain how to use your graph to find the total cost of renting a compact car for 7 days. Then find this cost. TRAVEL For Exercises 3 and 4, use the following information. Thomas is driving from Oak Ridge to Lakeview, a distance of 300 miles. He drives at a constant 60 miles per hour. The equation for the distance yet to go is y = 300 - 60x, where x is the number of hours since he left. 3. What is the slope and y-intercept? Explain how to use the slope and y-intercept to graph the equation. Then graph the equation. y x 0 12345 100 200 300 Distance (mi) Time (h) 4. What is the x-intercept? What does it represent? 5. WEATHER The equation y = 0.2x + 3.5 can be used to find the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day. Identify the slope and y-intercept of the graph of the equation and explain what each represents. 6. SALARY Janette’s weekly salary can be represented by the equation y = 500 + 0.4x, where x is the dollar total of her sales for the week. Identify the slope and y-intercept of the graph of the equation and explain what each represents. 3-2 Problem-Solving Practice Slope-Intercept Form 045_060_HPC3C3_892764.indd 52 45_060_HPC3C3_892764.indd 52 2/2/10 9:58:06 PM /2/10 9:58:06 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 53 Course 2 State the x- and y-intercepts of each function. 1. –6x + 8y = 24 2. 3 − 4 x – 6y = 18 3. - 1 − 4 x – 1 − 3 y = 12 4. –10x – 10y = –20 5. x + y = 1 6. –x – y = 1 − 2 State the x- and y- intercepts of each function. Then graph the function. 7. –4x + 2y = –8 8. 6x – 2y = –18 y 0 x 1 1 y 0 x 2 2 9. FARMING Mr. Jeans raises cows and chickens on his farm. Altogether, his cows and chickens have 140 legs. This can be represented by the function 4x + 2y = 140. Graph the function. Then interpret the x- and y-intercepts. 10. MONEY Monty has a total of $290 in ten dollar and five dollar bills. This can be represented by the function 10x + 5y = 290. Interpret the x- and y-intercepts. Get Connected Get Connected For more examples, go to glencoe.com. y 0 x 10 10 3-2 B Homework Practice Graph Functions Using Intercepts 045_060_HPC3C3_892764.indd 53 45_060_HPC3C3_892764.indd 53 2/2/10 9:58:12 PM /2/10 9:58:12 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 54 Course 2 1. FOOTBALL Tyrell plays running back and kicks field goals for his team. He scores 6 points for a touchdown and 3 points for a field goal. In his last game, he scored 24 points. This can be represented by the function 6x + 3y = 24. Find the x- and y-intercepts. Interpret the x- and y-intercepts. 2. GARDENING Mr. Bigelow’s garden is a rectangle with dimensions x feet long by y feet wide. Its perimeter is 70 feet. a. Write a function to represent the perimeter of his garden. b. What are the x- and y-intercepts of the function? c. Does either intercept make sense as a solution for this situation? Explain. 3. SCHOOL DANCE The sign below indicates the cost of attending the big dance. In all $320 was made. This can be represented by the function 2x + 5y = 320. Find the x- and y-intercepts. What do they represent? Dance Ticket Prices Fr./Soph. $2 Jr./Sr. $5 - intercept 160; -intercept 64; Sample answer: The -intercept indicates that 160 freshman/ sophomores attended the dance and that no juniors/seniors did. The y-intercept indicates that 64 juniors/ seniors attended the dance and that no freshman/sophomores did. 4. CONSTRUCTION Jack bought x picks costing $30 each and y shovels costing $40 each. In all he spent $240. a. Write a function to represent this situation. b. What are the x- and y-intercepts of the function? c. What do the intercepts represent? 5. BRICKS Jarrod is putting in a sidewalk using two different style bricks. One style brick is 8 inches long, and he intends to use x of these bricks. The other style brick is 6 inches long, and he intends to use y of these. His sidewalk is to be 288 inches long. a. Write a function to represent the length of his sidewalk. b. What are the x- and y-intercepts of the function? What do they represent? 3-2 B Problem-Solving Practice Graph Functions Using Intercepts 045_060_HPC3C3_892764.indd 54 45_060_HPC3C3_892764.indd 54 2/2/10 9:58:20 PM /2/10 9:58:20 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 55 Course 2 A For Exercises 1 and 2, solve using the guess, check, and revise strategy. 1. NUMBER THEORY A number is squared and the result is 676. Find the number. 2. CRAFTS Sabrina has 12 spools of ribbon. Each spool has either 3 yards of ribbon, 5 yards of ribbon, or 8 yards of ribbon. If Sabrina has a total of 68 yards of ribbon, how many spools of each length of ribbon does she have? Use any strategy to solve Exercises 3–7. Some strategies are shown below. PROBLEM-SOLVING STRATEGIES Guess, check, and revise. Draw a diagram. Make a table. Choose an operation. • • • • 3. NUMBERS Among all pairs of whole numbers with product 66, find the pair with the smallest sum. 4. SHOPPING You are buying a jacket that costs $69.95. If the sales tax rate is 7.75%, would it be more reasonable to expect the sales tax to be about $4.90 or $5.60? 5. STATES Of the 50 United States, 14 have coastlines on the Atlantic Ocean, 5 have coastlines on the Gulf of Mexico, and one state has coastlines on both. How many states do not have coastlines on either the Atlantic Ocean or the Gulf of Mexico? 6. TIME Melissa spent 7 1 − 2 minutes of the last hour downloading songs from the Internet. What percent of the last hour did she spend downloading songs? 7. VOLUNTEERING Greg helps his mother deliver care baskets to hospital patients each Saturday. Last Saturday at noon they had three times as many baskets left to deliver as they had already delivered. If they were delivering a total of 64 baskets that day, how many had they delivered by noon? Mixed Problem Solving 3-3 Homework Practice Problem-Solving Investigation: Guess, Check, and Revise Get Connected Get Connected For more examples, go to glencoe.com. 045_060_HPC3C3_892764.indd 55 45_060_HPC3C3_892764.indd 55 2/4/10 5:29:27 PM /4/10 5:29:27 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 56 Course 2 A Use the guess, check, and revise strategy to solve each problem. SKATES For Exercises 1 and 2, use the information below. It shows the income a sporting goods store received in one week for skate sharpening. Skate Sharpening Income for Week 6 Cost to Sharpen Hockey Skates Cost to Sharpen Figure Skates Total Pairs of Skates Sharpened Total Income from Skate Sharpening $6 a pair $4 a pair 214 $1,096 1. How many pairs of hockey skates and figure skates were sharpened during the week? 2. How much more did the sporting goods store earn sharpening hockey skates than figure skates? 3. FIELD TRIP At the science museum, the laser light show costs $2 and the aquarium costs $1.50. On a class field trip, each of the 30 students went to either the laser light show or the aquarium. If the teacher spent exactly $51 on tickets for both attractions, how many students went to each attraction? 4. NUMBERS Mr. Wahl is thinking of two numbers. The sum of the numbers is 27. The product of the numbers is 180. What two numbers is Mr. Wahl thinking of? 5. READING MARATHON Mrs. Johnson’s class broke the school reading record by reading a total of 9,795 pages in one month. Each student read a book that was either 245 pages or 360 pages. If 32 students participated in the reading marathon, how many students read each book? 6. REWARDS The soccer coaches bought gifts for all their soccer players. Gifts for the girls cost $4 each and gifts for the boys cost $3 each. There were 32 more boy soccer players than girl soccer players. If the coaches spent a total of $411 on gifts for their players, how many boys and girls played soccer? 3-3 Problem-Solving Practice Problem-Solving Investigation: Guess, Check, and Revise 045_060_HPC3C3_892764.indd 56 45_060_HPC3C3_892764.indd 56 2/2/10 9:58:28 PM /2/10 9:58:28 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 57 Course 2 Solve each system of equations by graphing. 1. y = 3x + 4 2. y = 10 + 6x y = -x - 4 y = 6x y O x y O x Write and solve a system of equations that represents each situation. Interpret the solution. 3. Alonzo and Miguel scored a total of 54 points in the basketball game. Miguel scored four more points than Alonzo. 4. Morgan is 15 years younger than Mrs. Santos. Their combined age is 44. 5. The total number of cats and dogs at the shelter is 125. There are 5 more cats than dogs. 6. Jenny won the ping-pong championship eight more times than Gerardo. They have won a combined total of 32 championships. y x O 56 40 24 8 4 12 20 28 y x O 56 40 24 8 4 12 20 28 y O x 56 40 24 8 4 12 20 28 y x O 140 100 60 20 10 30 50 70 Get Connected Get Connected For more examples, go to glencoe.com. 3-3 C Homework Practice Solve Systems of Equations by Graphing 045_060_HPC3C3_892764.indd 57 45_060_HPC3C3_892764.indd 57 2/2/10 9:58:31 PM /2/10 9:58:31 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 58 Course 2 1. PROFIT Mr. Blackwell’s company produces nuts and bolts. The total monthly profit for his company was $76,378. The profit earned from nuts was $3,428 more than the profit earned from bolts. 2. JEWELRY Julie has 81 pieces of jewelry. She has twice as many earrings as she has necklaces. 3. REFRESHMENTS The seventh grade class supplied bags of snacks and beverages for the school dance. They supplied 19 more beverages than bags of snacks. The dance was supplied with a total of 371 items. 4. SANDWICHES The hamburger shop sells 500 sandwiches each day. They sell 100 more hamburgers than they do chicken sandwiches. 5. DOGS Arnold dog weighs 10 pounds less than twice his brother’s dog. The dogs’ combined weight is 50 pounds. 6. STUDENTS There are 26 students in Mrs. Ortlieb’s class. There are two more boys than girls. y O x 50 150 200 100 250 300 350 400 100 Snacks Beverages 50 150 200 250 300 350 400 y O x 100 100 Sandwiches Hamburgers 200 300 400 500 600 700 800 900 200 300 400 500 600 700 800 900 y 0 x Arnold’s Dog (lbs) Brother’s Dog (lbs) 4 12 20 28 8 24 40 56 y x O 4 12 16 8 20 24 28 32 2 4 6 8 10 12 14 16 Girls Boys Write and solve a system of equations that represents each situation. Interpret the situation. y O x 8,000 31,000 16,000 24,000 32,000 40,000 48,000 56,000 64,000 Nuts Bolts 32,000 33,000 34,000 35,000 36,000 37,000 38,000 y O x 10 30 40 20 50 60 70 80 5 10 15 20 25 30 35 Necklaces Earrings 3-3 C Problem-Solving Practice Solve Systems of Equations by Graphing 045_060_HPC3C3_892764.indd 58 45_060_HPC3C3_892764.indd 58 2/2/10 9:58:45 PM /2/10 9:58:45 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 59 Course 2 Solve each system of equations by substitution. 1. y = x + 2 2. y = -x 3. y = -x - 4 y = -3x y = -7x y = x 4. y = x - 6 5. y = x + 5 6. y = x - 4 y = 2x y = -2x y = 2x 7. y = -x - 14 8. y = x + 20 9. y = -x - 3 y = -8x y = 6x y = 3x Write and solve a system of equations that represents each situation. Interpret the solution. 10. MONEY Neil has a total of twelve $5 and $10 bills in his wallet. He has 5 times as many $10 bills as $5 dollar bills. How many of each does he have? 11. HAYRIDE Hillary and 23 of her friends went on a hayride. There are 8 more boys than girls on the ride. How many boys and girls were on the ride? 12. DRIVING Winston drove a total of 248 miles on Monday. He drove 70 fewer miles in the morning than he did in the afternoon. How many miles did he drive in the afternoon? Get Connected Get Connected For more examples, go to glencoe.com. 3-3 D Homework Practice Solve Systems of Equations by Substitution 045_060_HPC3C3_892764.indd 59 45_060_HPC3C3_892764.indd 59 2/2/10 9:58:59 PM /2/10 9:58:59 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st Pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 60 Course 2 1. GEOMETRY The perimeter of a rectangle is 36 meters. The length of the rectangle is 4 meters longer than the width. Find the length and width of the rectangle. Interpret the solution. 2. WOOD Mildred cut a 9 foot board into two pieces. The long piece is twice as long as the short one. How long is the short piece? Interpret the solution. 3. SWIMMING POOLS Victor’s swimming pool holds 3,000 gallons. He filled the pool using two hoses. The larger hose filled the pool four times as fast as the smaller one. How many gallons of water came from the smaller hose? Interpret the solution. 4. FALL Julio bought a total of 20 medium and large pumpkins. If he spent $53 and bought 6 more large pumpkins as medium pumpkins, how many large pumpkins did he buy? Interpret the solution. 5. MUSIC Mr. Winkle downloaded 34 more songs than Mrs. Winkle downloaded. Together they downloaded 220 songs. How many songs did each download? Interpret the solution. 6. BAND The seventh and eighth grade bands held a joint concert. Together there were 188 band members. If the eighth grade band is 3 times as big as the seventh grade band, how big is the eighth grade band? Interpret the solution. 7. WORK Amal worked a total of 30 hours last week. On Saturday and Sunday he worked 5 times as many hours than he worked the rest of the week. How many hours did he work the rest of the week? Interpret the solution. 8. RAIN During the months of August and September the total rainfall was 6.2 inches. If the rainfall in August was 0.6 inch more than the amount of rainfall in September, how much rain fell in each month? Interpret the solution. Pumpkins Large - $3 Medium - $2 Small - $1 3-3 D Problem-Solving Practice Solve Systems of Equations by Substitution 045_060_HPC3C3_892764.indd 60 45_060_HPC3C3_892764.indd 60 2/2/10 9:59:06 PM /2/10 9:59:06 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 61 Course 3 4-1 A Use the work backward strategy to solve Exercises 1 and 2. 1. TRAVEL Rajiv and his family left home on a trip and drove for 2 hours before they stopped to eat. After 1.5 hours, they were back on the road. They arrived at their destination 3 hours later at 5:00 P.M. What time did they leave home? 2. GRADES Kumiko had an average of 92 on her first three math tests. Her scores on the second and third tests were 97 and 89. What was her score on the first test? Use any strategy to solve Exercises 3–6. Some strategies are shown below. Problem-Solving Strategies • Work backward. • Look for a pattern. • Choose an operation. 3. BAKING Isabel doubled her recipe for chocolate chip cookies. After her brothers ate 8 cookies, she set aside half of the remaining cookies for a school party. Isabel then gave 2 dozen cookies to her neighbor. She had 12 cookies left over. How many cookies does one recipe make? 4. ANALYZE TABLES The table below gives the results from a poll taken at school about the times in minutes that boys and girls spend using the Internet for school work and the total time spent using the Internet each week. Gender Time Used for School Work Total Time per Week Boys 33 min 255 min Girls 72 min 213 min How many more minutes per week do boys spend using the Internet for purposes other than school work than girls? 5. MOVIES The two animated films with the highest box office receipts brought in a total of $775 million. If one film brought in $97 million more than the other, how much did the film with the highest receipts bring in? 6. U.S. PRESIDENTS Harry S. Truman was elected vice president in 1944. He died in 1972 at the age of 88. How old was he at the time he was elected? Mixed Problem Solving Get Connected Get Connected For more examples, go to glencoe.com. Homework Practice Problem-Solving Investigation: Work Backward 061_082_HPC3C4_892764.indd 61 61_082_HPC3C4_892764.indd 61 2/2/10 9:59:29 PM /2/10 9:59:29 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 62 Course 3 4-1 A 1. How many minutes did Elena practice the clarinet on Thursday? 2. How many minutes did Elena practice on Monday? 3. HOCKEY During a hockey game, Brandon played 7 less minutes than Nick. Zach played 12 minutes more than Brandon. Hunter played twice as long as Zach. Hunter played for 44 minutes. How many minutes did Nick play in the hockey game? 4. PACKAGES In the morning, a delivery truck delivers 24 of its packages to a factory. It then goes to a distribution lot, where the remaining packages are separated into 4 equal groups and put on other trucks. There were 18 packages in each of the groups. How many packages were on the delivery truck to begin with? 5. WEATHER On Monday, Eliza read her book. On Tuesday, she read three times as long as she read on Monday. On Wednesday she read 20 minutes less than Tuesday. On Thursday she read for 20 minutes, which was half as long as she read on Wednesday How many minutes did Eliza read over the 4-day period? 6. STAMPS Zoe added 23 stamps to her collection. Three months later her collection had tripled in number to a total of 159 stamps. How many stamp did Zoe have to start her collection? Use the work backward strategy to solve each problem. CLARINET PRACTICE For Exercises 1 and 2, use the table below. It is a record of the amount of time Elena practiced her clarinet in a week. Monday Tuesday Thursday Saturday Sunday ? 20 minutes more than Monday 10 minutes less than Tuesday Twice as long as Thursday 15 minutes less than Saturday– 45 minutes Problem-Solving Practice Problem-Solving Investigation: Work Backward 061_082_HPC3C4_892764.indd 62 61_082_HPC3C4_892764.indd 62 2/2/10 9:59:43 PM /2/10 9:59:43 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 63 Course 3 4-1 Define a variable. Then write an equation to model each situation. 1. After receiving $25 for her birthday, Latisha had $115. 2. At 14 years old, Adam is 3 years younger than his brother Michael. 3. A class of 30 students separated into equal sized teams results in 5 students per team. 4. When the bananas were divided evenly among the 6 monkeys, each monkey received 4 bananas. Define a variable. Then write an equation that could be used to solve each problem. 5. GRADES Kelly’s test score was 6 points higher than Micheline’s. If Kelly’s test score was 88, what was Micheline’s test score? 6. GEOMETRY A rectangle’s width is one-third its length. If the width is 8 inches, what is the length of the rectangle? 7. FOOTBALL A team had a total gain of -15 yards over several plays with an average gain of -5 yards per play. How many plays are represented? Write an equation to model the relationship between the quantities in each table. 8. Kilograms, k Grams, g 1 1,000 2 2,000 3 3,000 4 4,000 k g 9. Feet, f Yards, y 3 1 6 2 9 3 12 4 f y 10. MONEY Carlotta earns $3 for every hour that she baby sits. Complete the table of values showing the amount she earns for baby sitting 1, 2, 3, 4, and h hours. Given h, a number of hours, write an equation to find a, the amount that Carlotta earns. Get Connected Get Connected For more examples, go to glencoe.com. Hours, h Amount, a Homework Practice Write Equations B 061_082_HPC3C4_892764.indd 63 61_082_HPC3C4_892764.indd 63 2/2/10 9:59:46 PM /2/10 9:59:46 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 64 Course 3 4-1 1. AGE Julia is 3 years younger than Kevin. Kevin is 13. Define a variable and write an equation to find Julia’s age. 2. CIVICS In the 2008 presidential election, Florida had 23 more electoral votes than Idaho. Define a variable and write an equation to find the number of Idaho’s electoral votes if Florida had 27 votes. 3. ENERGY One year, China consumed 4 times as much energy as Brazil. Define a variable and write an equation to find the amount of energy Brazil used that year if China used 2,000 billion kilowatt-hours. 4. CHEMISTRY The atomic number of cadmium is half the atomic number of curium. The atomic number for cadmium is 48. Define a variable and write an equation to find the atomic number of curium. 5. LIBRARIES The San Diego Public Library has 44 fewer branches than the Chicago Public Library. Define a variable and write an equation for the number of branches in the San Diego Public Library if Chicago has 79 branches. 6. ASTRONOMY Saturn is 6 times farther from the Sun than Mars. Define a variable and write an equation to find the distance of Mars from the Sun if Saturn is about 1,429,400,000 km from the sun. 7. POPULATION The estimated population of Jacksonville, Florida, is 401,868 more than the population of Omaha, Nebraska. Omaha has an estimated population of 432,921. Define a variable and write an equation to find the population of Jacksonville. 8. GEOGRAPHY Kings Peak in Utah is 8,667 feet taller than Spruce Knob in West Virginia. Spruce Knob is 4,861 feet tall. Define a variable and write an equation to find the height of Kings Peak. B Problem-Solving Practice Write Equations 061_082_HPC3C4_892764.indd 64 61_082_HPC3C4_892764.indd 64 2/2/10 9:59:50 PM /2/10 9:59:50 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 65 Course 3 4-1 Solve each equation. Check your solution. 1. t + 7 = 12 2. h - 3 = 8 3. 8 = b - 9 4. k - 4 = -14 5. m + 9 = -7 6. y - 10 = -3 7. -14 = 2 + d 8. 15 + n = 10 9. -8 = r - 6 10. 11 = w - 5 11. -9 = g + 9 12. 12 + c = 16 13. GEOMETRY Two angles are supplementary if the sum of their measures is 180°. The two angles shown are supplementary. Write and solve an equation to find the measure of angle R. 14. ARCHITECTURE The Sears Tower in Chicago was the tallest building in the world when it was completed. Twenty-three years later, a taller building was completed in 1996 in Taiwan. Write and solve an equation to find the year that the Sears Tower was completed. 15. FUNDRAISING During a five-day fundraiser, Shantell sold 8 boxes of greeting cards the first day, 6 boxes the second day, 10 boxes the third day, and 7 boxes the fourth day. If she sold a total of 45 boxes of greeting cards during the five days, write an equation that can be used to find the number of boxes Shantell sold the fifth day. Explain two methods of solving this equation. Then solve the equation. 16. ANALYZE TABLES The total points scored by both teams in the 2008 Super Bowl was 15 less than the total points for 2007. Write and solve an equation to find the total points for 2007. R S 140 Total Points Scored by Both Teams in Super Bowl Year Points 2007 p 2008 31 Get Connected Get Connected For more examples, go to glencoe.com. C Homework Practice Solve Addition and Subtraction Equations 061_082_HPC3C4_892764.indd 65 61_082_HPC3C4_892764.indd 65 2/2/10 9:59:54 PM /2/10 9:59:54 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 66 Course 3 4-1 180‚ m∠"
= 78‚ # " 1. AGE Walter lived 2 years longer than his brother Martin. Walter was 79 at the time of his death. Write and solve an addition equation to find Martin’s age at the time of his death. 2. CIVICS Florida has 28 fewer members in the House of Representatives than California. Florida has 25 representatives. Write and solve a subtraction equation to find the number of California representatives. 3. GEOMETRY Two angles are supplementary if the sum of their measures is 180°. Angles A and B are supplementary. If the measure of angle A is 78°, write and solve an addition equation to find the measure of angle B. 4. BANKING After you withdraw $40 from your checking account, the balance is $287. Write and solve a subtraction equation to find your balance before this withdrawal. 5. WEATHER After the temperature had risen 12°F, the temperature was 7°F. Write and solve an addition equation to find the starting temperature. 6. CHEMISTRY The atomic number of mercury is the sum of the atomic number of aluminum and 67. The atomic number of mercury is 80. Write and solve an addition equation to find the atomic number of aluminum. 7. ELEVATION The lowest point in Louisiana is 543 feet lower than the highest point in Louisiana. The elevation of the lowest point is -8 feet. Write and solve a subtraction equation to find the elevation of the highest point in Louisiana. 8. POPULATION In 2008, the estimated population of Honduras was the estimated population of Haiti decreased by 7,639,327. The population of Honduras was 1,285,226. Write and solve a subtraction equation to find the population of Haiti. 7° F C Problem-Solving Practice Solve Addition and Subtraction Equations 061_082_HPC3C4_892764.indd 66 61_082_HPC3C4_892764.indd 66 2/2/10 9:59:58 PM /2/10 9:59:58 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 67 Course 3 4-1 Solve each equation. Check your solution. 1. 5s = 45 2. 8h = 64 3. 36 = 9b 4. -3p = 24 5. -12m = -72 6. -56 = 7d 7. − x 35 = 11 8. v − 4 = 20 9. − c -12 = 43 10. 16 = y − -3 11. -9 = n − 8 12. − a 25 = -13 13. CARS Mrs. Alvarez bought a new car. Her monthly payments are $525. If she will pay a total of $25,200 in payments, write and solve a multiplication equation to find the number of payments. 14. POPULATION The projected population of South Africa in 2010 is four times the projected population of Zambia. If the projected population of South Africa in 2010 is 48 million, write and solve a multiplication equation to find the projected population of Zambia. 15. MEASUREMENT Refer to the table. Write and solve an equation to find each quantity. a. the number of quarts in 24 pints b. the number of gallons in 104 pints Solve each equation. 16. 3 = − -84 g 17. − -4 x = -8 18. − -144 r = -16 Get Connected Get Connected For more examples, go to glencoe.com. Customary System Conversions (capacity) 1 pint = 2 cups 1 quart = 2 pints 1 quart = 4 cups 1 gallon = 4 quarts 1 gallon = 8 pints D Homework Practice Solve Multiplication and Division Equations 061_082_HPC3C4_892764.indd 67 61_082_HPC3C4_892764.indd 67 2/2/10 10:00:05 PM /2/10 10:00:05 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 68 Course 3 4-1 1. WAGES Felipe earns $9 per hour for helping his grandmother with her yard work. Write and solve a multiplication equation to find how many hours he must help his grandmother in order to earn $54. 2. SHOPPING Granola bars are on sale for $0.50 each. If Brad paid $5 for granola bars, write and solve a multiplication equation to find how many bars he bought. 3. EXERCISE Jasmine jogs 3 miles each day. Write and solve a multiplication equation to find how many days it will take her to jog 57 miles. 4. TRAVEL On a trip, the Rollins family drove at an average rate of 62 miles per hour. Write and solve a multiplication equation to find how long it took them to drive 558 miles. 5. ROBOTS The smallest robot can travel 20 inches per minute through a pipe. Write and solve a multiplication equation to find how long it will take this robot to travel through 10 feet of pipe. 6. BANKING Nate withdraws $40 from his checking account each day. Write and solve a multiplication equation to find how long it will take him to withdraw $680. 7. AGE The product of Bart’s age and 26 is 338. Write and solve a multiplication equation to find Bart’s age. 8. POPULATION The population of a small town is increasing at a rate of 325 people per year. Write and solve a multiplication equation to find how long it will take the population to increase by 6,825. D Problem-Solving Practice Solve Multiplication and Division Equations 061_082_HPC3C4_892764.indd 68 61_082_HPC3C4_892764.indd 68 2/2/10 10:00:09 PM /2/10 10:00:09 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 69 Course 3 Solve each equation. Check your solution. 1. 3g + 5 = 17 2. 9 = 4a + 13 3. 13 = 5m - 2 4. -15 = 2t - 11 5. 7k - 5 = -19 6. 13 = 4x -11 7. 10 = z − 2 + 7 8. 6 + n − 5 = -4 9. 4 - 3y = 31 10. 15 - 2b = -9 11. - 1 − 3 y - 6 = -11 12. 16 - r − 7 = 21 13. 30 = 5d - 8d 14. w + 3w = 20 15. 5 - 7m + 9m = 11 16. -18 = 8x - 9 - 5x 17. 25 = s + 13 - 4s 18. 6a + 7 - a = -18 19. 3(y + 5) = 21 20. 7(p - 3) = 35 21. -48 = 6(v + 2) 22. − k - 3 4 = 10 23. − z + 5 7 = -3 24. − 9 + t 12 = -3 25. SHOPPING Mrs. Williams shops at a store that has an annual membership fee of $30. Today she paid her annual membership and bought several fruit baskets costing $15 each as gifts for her coworkers. Her total was $105. Solve the equation 15b + 30 = 105 to find the number of fruit baskets Mrs. Williams purchased. 26. GAMES A card game has 50 cards. After dealing 7 cards to each player, Tupi has 15 cards left over. Solve the equation 50 - 7p = 15 to find the number of players. 27. GEOMETRY Write an equation to represent 28 12 y 3y P Q the length of −−− PQ . Then find the value of y. Get Connected Get Connected For more examples, go to glencoe.com. 4-2 B Homework Practice Solve Two-Step Equations 061_082_HPC3C4_892764.indd 69 61_082_HPC3C4_892764.indd 69 2/2/10 10:00:12 PM /2/10 10:00:12 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 70 Course 3 1. SHOPPING Jenna bought 5 reams of paper at the store for a total of $21. The tax on her purchase was $1. Solve 5x + 1 = 21 to find the price for each ream of paper. 2. CARS It took Lisa 85 minutes to wash three cars. She spent x minutes on each car and 10 minutes putting everything away. Solve 3x + 10 = 85 to find how long it took to wash each car. 3. EXERCISE Cole jogged the same distance on Tuesday and Friday, and 8 miles on Sunday, for a total of 20 miles for the week. Solve 2x + 8 = 20 to find the distance Cole jogged on Tuesday and Friday. 4. MOVING Heather has a collection of 26 mugs. When packing to move, she put the same number of mugs in each of the first 4 boxes and 2 mugs in the last box. Solve 4x + 2 = 26 to find the number of mugs in each of the first four boxes. 5. TELEVISION Burt’s parents allow him to watch a total of 10 hours of television per week. This week, Burt is planning to watch several two–hour movies and four hours of sports. Solve 2x + 4 = 10 to find the number of movies Burt is planning to watch this week. 6. TRAVEL Lawrence drives the same distance Monday through Friday commuting to work. Last week, Lawrence drove 25 miles on the weekend, for a total of 60 miles for the week. Solve 5x + 25 = 60 to find the distance Lawrence drives each day commuting to work. 7. MONEY McKenna had $32 when she got to the carnival. After riding 6 rides, she had $20 left. Solve 32 - 6x = 20 to find the price for each ride. 8. GARDENING Jack has 15 rosebushes. He has the same number of yellow, red, and pink bushes, and 3 multicolored bushes. Solve 3x + 3 = 15 to find the number of yellow rosebushes Jack has. B 4-2 Problem-Solving Practice Solve Two-Step Equations 061_082_HPC3C4_892764.indd 70 61_082_HPC3C4_892764.indd 70 2/2/10 10:00:16 PM /2/10 10:00:16 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 71 Course 3 Translate each sentence into an equation. 1. Three more than eight times a number is equal to 19. 2. Twelve less than seven times a number is 16. 3. Four more than twice a number is -10. 4. Nine less than five times a number is equal to -30. 5. ART Ishi bought a canvas and 8 tubes of paint for $24.95. If the canvas cost $6.95, how much did each tube of paint cost? 6. ENGINEERING The world’s two highest dams are both in Tajikistan. The Rogun dam is 35 meters taller than the Nurek dam. Together they are 635 meters tall. Find the height of the Nurek dam. 7. U.S. PRESIDENTS Use the information at the right. a. If you double President Reagan’s age at the time of his first inauguration and subtract his age at the time he died, the result is 45 years. How old was President Reagan when he died? b. If you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years, you get the age of President Clinton when he was first inaugurated. How old was President G. H. W. Bush when he was inaugurated? 8. GEOMETRY Find the value of x in the triangle at 36° x° x° the right. 9. ALGEBRA Three consecutive integers can be represented by n, n + 1, and n + 2. If the sum of three consecutive integers is 57, what are the integers? Get Connected Get Connected For more examples, go to glencoe.com. President Age at First Inauguration J. Carter 52 R. Reagan 69 G. H. W. Bush ? W. Clinton 46 G. W. Bush 54 4-2 C Homework Practice Write Two-Step Equations 061_082_HPC3C4_892764.indd 71 61_082_HPC3C4_892764.indd 71 2/2/10 10:00:19 PM /2/10 10:00:19 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 72 Course 3 1. CONSTRUCTION Carlos is building a screen door. The height of the door is 1 foot more than twice its width. What is the width of the door if it is 7 feet high? 2. GEOMETRY A rectangle has a width of 6 inches and a perimeter of 26 inches. What is the length of the rectangle? 3. EXERCISE Ella swims four times a week at her club’s pool. She swims the same number of laps on Monday, Wednesday, and Friday, and 15 laps on Saturday. She swims a total of 51 laps each week. How many laps does she swim on Monday? 4. SHOPPING While at the music store, Drew bought 5 CDs, all at the same price. The tax on his purchase was $6, and the total was $61. What was the price of each CD? 5. STUDYING Over the weekend, Koko spent 2 hours on an assignment, and she spent equal amounts of time studying for 4 exams for a total of 16 hours. How much time did she spend studying for each exam? 6. FOOD At the market, Meyer buys a bunch of bananas for $0.65 per pound and a frozen pizza for $4.99. The total for his purchase was $6.94, without tax. How many pounds of bananas did Meyer buy? 7. HOME IMPROVEMENT Laura is making a patio in her backyard using paving stones. She buys 44 paving stones and a flowerpot worth $7 for a total of $73. How much did each paving stone cost? 8. TAXI A taxi service charges you $1.50 plus $0.60 per minute for a trip to the airport. The distance to the airport is 10 miles, and the total charge is $13.50. How many minutes did the ride to the airport take? Write and solve an equation to solve each problem. 4-2 C Problem-Solving Practice Write Two-Step Equations 061_082_HPC3C4_892764.indd 72 61_082_HPC3C4_892764.indd 72 2/2/10 10:00:23 PM /2/10 10:00:23 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 73 Course 3 A Write an inequality for each sentence. 1. Applicants with less than 5 years of experience must take a test. 2. The home team needs more than 6 points to win. 3. The minimum voting age is 18. 4. You must answer at least 10 questions correctly to stay in the game. 5. A tip of no less than 10% is considered acceptable. 6. The cost including tax is no more than $75. Graph each inequality on a number line. 7. y > 5 012345678 8. h < 5 123 45678 9 9. c ≤ 1 -4 -3 -2 -10 1 2 3 4 10. t ≥ 2 -2 -101 2345 6 11. x ≥ 4 1234 5678 9 12. r < 9 4 5 6 7 8 9 10 11 12 State whether the inequality is true or false for the given value. 13. 9 + b < 16, b = 8 14. 14 - f > 8, f = 5 15. -5t < 24, t = 5 16. 51 ≤ 3m, m = 17 17. z − 5 ≤ 7, z = 40 18. − -28 d > 7, d = -4 19. Use the table that shows the literacy rate in several countries. a. In which country or countries is the literacy rate less than 90%? b. In which country or countries is the literacy rate at least 88%? Country Literacy Rate Albania 87% Jamaica 88% Panama 93% Senegal 40% 4-3 Homework Practice Graph Inequalities 061_082_HPC3C4_892764.indd 73 61_082_HPC3C4_892764.indd 73 2/2/10 10:00:26 PM /2/10 10:00:26 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 74 Course 3 A 1. SPORTS Colin’s time in the 400-meter run was 62 seconds. Alvin was at least 4 seconds ahead of Colin. Write an inequality for Alvin’s time in the 400-meter run. 2. RESTAURANTS Before Valerie and her two friends left Mel’s Diner, there were more than 25 people seated. Write an inequality for the number of people seated at the diner after Valerie and her two friends left. 3. FARM LIFE Reggie has 4 dogs on his farm. One of his dogs, Lark, is about to have puppies. Write an inequality for the number of dogs Reggie will have if Lark has fewer than 4 puppies. 4. MONEY Alicia had $25 when she arrived at the fair. She spent t dollars on ride tickets and she spent $6.50 on games. Write an inequality for the amount of money Alicia had when she left the fair. 5. HEALTH Marcus was in the waiting room for 26 minutes before being called. He waited at least another 5 minutes before the doctor entered the examination room. Write an inequality for the amount of time Marcus waited before seeing the doctor. 6. POPULATION The population of Ellisville was already less than 250 before Bob and Ann Tyler and their three children moved away. Write an inequality for the population of Ellisville after the Tyler family left. 7. HOMEWORK Nova spent one hour on Thursday, one hour on Saturday, and more than 2 hours on Sunday working on her writing assignment. Write an inequality for the amount of time she worked on the assignment. 8. YARD WORK Harold was able to mow more than 3 − 4 of his lawn on Saturday night. Write an inequality for the fraction of the lawn that Harold will mow on Sunday. 4-3 Problem-Solving Practice Graph Inequalities 061_082_HPC3C4_892764.indd 74 61_082_HPC3C4_892764.indd 74 2/2/10 10:00:32 PM /2/10 10:00:32 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 75 Course 3 Solve each inequality. Graph the solution on a number line. 1. n + 4 < 9 2. t + 7 > 12 1 67 2 3 4 5 9 8 1 67 2 3 4 5 9 8 3. p + (-5) > -3 4. -13 ≤ x - 8 1 67 2 3 4 5 9 8 -7 -6 -5 -4 -3 -2 -101 5. -32 ≥ a + (-5) 6. 3 ≤ 1 − 2 + m -30 -28 -26 -24 -22 0 3 1 2 4 7. 4 ≥ s - 2 − 3 8. - 3 − 4 < w - 1 3 5 4 1 – 2 012 1 – 2 1 Write an inequality and solve each problem. 9. Five less than a number is more than twenty. 10. Four more than a number is no more than twelve. 11. The sum of a number and 3.5 is at least 14.5. 12. The difference of a number and -5 is less than 7. 13. The sum of -12 and a number is at least 6. 14. Eleven less than a number is more than fifteen. 15. CARNIVALS Carol wants to ride the bumper cars, but the sign says that she needs to be at least 42 inches tall. Write and solve an inequality that describes how many inches she needs to grow if she is currently 33 inches tall. 16. CANDY Karl had a total of 45 chocolate bars to give away. He had already given away 26 of them. Write and solve an inequality that describes how many more candy bars at most he has to give away. 17. AGE Sergio is no older that 18 but is 5 years older than Marco. Write and solve an inequality that describes the possibilities for Marco's age. Get Connected Get Connected For more examples, go to glencoe.com. 4-3 B Homework Practice Solve Inequalities by Addition or Subtraction 061_082_HPC3C4_892764.indd 75 61_082_HPC3C4_892764.indd 75 2/2/10 10:00:36 PM /2/10 10:00:36 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 76 Course 3 1. DRIVING Michael is driving from Lakeview to Dodge City, a distance of more than 250 miles. After driving 60 miles, Michael stops for gas. Write and solve an inequality to find how much farther Michael has to drive to reach Dodge City. 2. ENTERTAINMENT Kelvin and Marsha are going to dinner and a movie this evening. Kelvin wants to have at least $70 cash in his wallet. He currently has $10. Write and solve an inequality to find how much cash Kelvin should withdraw from the bank. 3. CLUBS The charter for the Spartan Club limits the membership to 85. Currently, the club has 47 members. Write and solve an inequality to find how many more members can be recruited. 4. GROWTH Akira hopes that he will someday be more than 71 inches tall. He is currently 63 inches tall. Write and solve an inequality to find how much more Akira must grow to fulfill his wish. 5. MUSIC Jamie is preparing to burn a music CD. The CD holds at most 70 minutes of music. Jamie has 52 minutes of music already selected. Write and solve an inequality to find how many more minutes of music Jamie can select. 6. TELEVISION Dario limits his TV watching to no more than 11 hours a week. This week, he has already watched 6 hours of TV. Write and solve an inequality to find how much more time Dario can spend watching TV this week. 7. CARS At the gas station, Elena bought a quart of oil for $1.50, and she filled her car with gas. Her total was less than $20. Write and solve an inequality to find how much she spent on gas. 8. HOMEWORK Peter must write an essay with more than 500 words for his English class. So far, he has written 245 words. Write and solve an inequality to find how many more words Peter needs to write for his essay. 4-3 B Problem-Solving Practice Solve Inequalities by Addition or Subtraction 061_082_HPC3C4_892764.indd 76 61_082_HPC3C4_892764.indd 76 2/2/10 10:00:44 PM /2/10 10:00:44 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 77 Course 3 Solve each inequality. Graph the solution on a number line. 1. -8 ≤ 4w 2. -6a > -78 -4 -3 -2 -1 01234 10 12 14 16 18 3. -25t ≤ 400 4. 18 > -2g -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 5. y − 4 ≥ 2.4 6. − r -2 < -2 9.0 9.2 9.4 9.6 9.8 1357 2 4 6 89 7. -8 > − k -0.4 8. − m -7 ≤ 1.2 3 3.2 3.4 3.6 3.8 -9 -8.6 -8.2 -7.8 -7.4 9. 13a ≤ -26 10. -15 ≤ 5b -6 -4 -2 0 2 -6 -5 -4 -3 -2 -1 0 1 2 11. KAYAKING Junior wants to go kayaking at least 8 hours each week. If he averages 2 hours per day, write and solve an inequality to find how many days he will have to go kayaking. 12. WEIGHT LIFTING Ariel wants to spend no more than 4 hours per week lifting weights. If she lifts Monday through Saturday, write and solve an inequality to find the maximum number of hours per day she can lift. Get Connected Get Connected For more examples, go to glencoe.com. 4-3 C Homework Practice Solve Inequalities by Multiplication or Division 061_082_HPC3C4_892764.indd 77 61_082_HPC3C4_892764.indd 77 2/2/10 10:00:47 PM /2/10 10:00:47 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 78 Course 3 1. PLANTS Monroe needs more than 45 cubic feet of soil to fill the planter he built. Each bag of soil contains 2.5 cubic feet. Write and solve an inequality to find how many bags of soil Monroe will need. 2. ART Lois is making a rectangular collage. The area of the rectangle is 255 square inches, and the area of each photo is 15 square inches. She will overlap the photos so the total area of the photos is more than 255 square inches. Write and solve an inequality to find how many photos Lois will need. 3. CAR WASH Jason’s class is having a car wash to raise money for a project. They want to raise at least $120, and they are charging $5 to wash a car. Write and solve an inequality to find how many cars must be washed to raise $120. 4. PETS Kendra wants to buy some goldfish for her fish tank. She can spend no more than $18, and the fish cost $3 each. Write and solve an inequality to find how many goldfish Kendra can buy. 5. PIZZA Trent and three of his friends are ordering a pizza. They plan to split the cost, and they want to spend at most $3.50 per person. Write and solve an inequality to find the cost of the pizza they should order. 6. GEOMETRY You are asked to draw a rectangle with a length of 6 inches and an area less than 30 square inches. Write and solve an inequality to find the width of the rectangle. 7. CONSTRUCTION Melinda wants to have a picture window in the shape of a regular hexagon in her new home. She wants the perimeter of the hexagon to be at least 9 feet. Write and solve an inequality to find the length of each side of the hexagon. 8. COOKING Len wants to make several batches of cookies. He is starting with less than 2 cups of raisins, and each batch takes 1 − 3 of a cup. Write and solve an inequality to find how many batches of cookies Len can make. 4-3 C Problem-Solving Practice Solve Inequalities by Multiplication or Division 061_082_HPC3C4_892764.indd 78 61_082_HPC3C4_892764.indd 78 2/2/10 10:00:58 PM /2/10 10:00:58 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 79 Course 3 A Solve each inequality. Graph the solution set on a number line. 1. 4x - 3 < 9 2. –11 ≥ -1 - 2x -10 4 5 6 7 1 2 3 123 89 4 5 6 7 3. -2 + 2x > -16 4. -3x + 2 ≤ 17 -11-10 -9 -8 -7 -6 -5 -4 -3 -9 -8 -7 -6 -5 -4 -3 -2 -1 5. 7 < x − 2 + 4 6. x − 5 - 1 ≥ - 2 2 3 8 9 10 4 5 6 7 -9 -8 -7 -6 -5 -4 -3 -2 -1 7. -4 ≤ 4x + 8 8. -3x -3 > 12 -7 -6 -5 -4 -3 -2 -101 -9 -8 -7 -6 -5 -4 -3 -2 -1 9. RENTAL BICYCLES A rental company charges $15 plus $4 per hour to rent a bicycle. If Margie does not want to spend more than $27 for her rental, write and solve an inequality to find how many hours she can rent the bicycle and not spend more than $27. Interpret the solution. 10. MOWING GRASS Rupesh is mowing grass to save money for a vacation. He charges $12 per yard. Rupesh already has $40 and wants to have at least $148 to take with him. Write and solve an inequality to determine how many yards Rupesh needs to mow to have at least $148. Interpret the solution. Get Connected Get Connected For more examples, go to glencoe.com. 4-4 Homework Practice Solve Two-Step Inequalities 061_082_HPC3C4_892764.indd 79 61_082_HPC3C4_892764.indd 79 2/2/10 10:01:02 PM /2/10 10:01:02 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 80 Course 3 A 1. CLOTHING Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an hour babysitting. Write and solve an inequality to find how many hours she will need to babysit to buy the dress. Interpret the solution. 2. SAVINGS Tameca already has $55 dollars in her savings account. If she puts $5 per week in her account, write and solve an inequality to find out how many weeks she must save to have at least $100 in her account. Interpret the solution. 3. COMMISSION Manuel earns $400 per week plus a 3% commission on everything he sells. Write and solve an inequality to find out how much he must sell to have a weekly income of at least $700. Interpret the solution. 4. CARS Remington needs at least $3,000 to buy a used car. He already has $1,800. If he saves $50 per week, write and solve an inequality to find out how many weeks he must save to buy the car. Interpret the solution. 5. POSTCARDS Latrell has $8 to spend on postcards. He wants to buy one large postcard and some small ones. Write and solve an inequality to find out how many small postcards Latrell can purchase. Interpret the solution. 1.25 + 2 ≤ 8, ≤ 4.8; Latrell can buy at most 4 small post cards. 6. CARRIAGE RIDE You want to spend at most $12 on a carriage ride. The driver tells you there is an initial charge of $5 plus $0.50 per mile. Write and solve an inequality to find out how many miles you can ride. Interpret the solution. 7. BAKING Corey has 16 cups of flour to make cookies. One batch of cookies takes 2 1 − 2 cups of flour. If he must save 6 cups of flour for other baking, write and solve an inequality to find out how many batches of cookies he can make. Interpret the solution. 8. ENTERTAINMENT Sylvia needs at least $310 for a new audio system. She has already saved $120. She earns $10 per hour at her part-time job. Write and solve an inequality to find how many hours she will need to work to buy the system. Interpret the solution. Postcards Large $2 Medium $1.50 Small $1.25 4-4 Problem-Solving Practice Solve Two-Step Inequalities 061_082_HPC3C4_892764.indd 80 61_082_HPC3C4_892764.indd 80 2/2/10 10:01:12 PM /2/10 10:01:12 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 81 Course 3 Get Connected Get Connected For more examples, go to glencoe.com. 1. NUMBERS A number is greater than or equal to –5 but less than 13. Write a compound inequality to represent this situation. 2. BICYCLES Proper tire inflation for a 26-inch bicycle is between 50 pounds per square inch and 55 pounds per square inch. Write a compound inequality that represents the values for which a tire is improperly inflated. Graph the solution set of each inequality. 3. t < 5 or t > 7 12 5 3 67 4 8 9 12 10 13 11 4. a > –2 and a ≤ 4 -5 -4 -3 -2 25 -1 0 1 3 67 4 5. n ≥ 12 or n < 8 5 9 6 7 8 12 15 10 11 13 16 17 14 6. g ≥ 17 and g < 21 14 18 15 16 17 21 24 19 20 22 25 26 23 7. m ≤ 9 or m > 13 6 9 7 8 12 15 10 11 13 16 17 18 14 8. k > 7 and k ≤ 11 3 9 4 5 6 7 8 12 15 10 11 13 14 Write a compound inequality for each graph. 9. -3 01 9 -2 -1 2 3 4 5 6 7 8 10. 4 7 8 16 5 6 9 10 11 12 13 14 15 4-4 B Homework Practice Compound Inequalities 061_082_HPC3C4_892764.indd 81 61_082_HPC3C4_892764.indd 81 2/2/10 10:01:16 PM /2/10 10:01:16 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 4 82 Course 3 Use the following table for Exercises 1 and 2. The Saffir-Simpson Tornado Scale assigns a rating to a tornado based on the tornado’s wind speed. Saffir-Simpson Tornado Scale Category Wind Speed (mph) F1 73–112 F2 113–157 F3 158–206 F4 207–260 F5 261–318 1. TORNADO Write a compound inequality representing the wind speed of an F3 tornado. 2. TORNADO Write a compound inequality representing the wind speed of an F3 or F4 tornado. 3. WORLD RECORDS According to the 2009 Guinness Book of World Records, Bao Xishun was the tallest living man at 7.9 feet and He Pingping was the shortest living man at 2.4 feet. Write a compound inequality representing the height range of men in the world in 2009. 4. AIRPLANES The Boeing 747, commonly called a jumbo jet, has four jet engines which propel the plane to cruising speeds of between 500 and 900 kilometers per hour. Write a compound inequality which represents speeds that are not cruising speeds for the Boeing 747. 5. CEILING HEIGHTS Zoie lives in a home that has a vaulted ceiling in the family room. At one end the ceiling is 8 feet high and at the opposite end the ceiling is 12 feet high. Write a compound inequality representing the height range of the ceiling. 6. CLIMATE As of 2008, the coldest air temperature ever recorded on Earth was –129° F. It was recorded in 1983 in Vostok, Antarctica. The warmest air temperature ever recorded on Earth was 136° F. It was recorded in 1922 at Al’ Aziziyah, Libya. Write a compound inequality which represents temperatures outside of these two extremes. 4-4 B Problem-Solving Practice Compound Inequalities 061_082_HPC3C4_892764.indd 82 61_082_HPC3C4_892764.indd 82 2/2/10 10:01:24 PM /2/10 10:01:24 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 83 Course 2 5-1 A Write each expression using exponents. 1. 3 3 m 2. (1 − 4)(1 − 4)(1 − 4) 3. 2 d 5 d d 5 4. p (-9) p (-9) p q q 5. g (-7) (-7) g h (-7) h 6. x 1 − 8 x x y 1 − 8 y x Evaluate each expression. 7. (-8)4 8. (1 − 5) 3 9. (- 3 − 5) 5 10. (-2)3 + 52 11. 34 - 52 12. (-2)5 - (-2)4 13. 43 ÷ 23 14. 53 23 15. 17 + (-3)4 ALGEBRA Evaluate each expression. 16. r3 - s, if r = 5 and s = 4 17. m2 - n3 , if m = 6 and n = 2 18. f - g4 , if f = 3 and g = -5 19. (x5 - y2 ) 2 + x3 , if x = 2 and y = 8 20. Replace with <, >, or = to make a true statement: 24 42 . 21. ISLANDS Florida has about 22 32 53 islands (over 10 acres). About how many islands is this? Get Connected Get Connected For more examples, go to glencoe.com. Homework Practice Powers and Exponents 083_102_HPC3C5_892764.indd 83 83_102_HPC3C5_892764.indd 83 2/2/10 10:01:46 PM /2/10 10:01:46 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 84 Course 2 5-1 A 1. GEOMETRY The volume of a cube can be found by raising the side length to the third power. What is the volume of the cube below? 14 in. 2. SPORTS In the first round of a local tennis tournament, there are 25 matches. Find the number of matches. 3. PALM TREES There are about 23 3 53 species of palm trees in the whole world. About how many species is this? 4. NATURE A forest fire affected about 34 104 acres of land. About how many acres did the fire affect? 5. BIOLOGY A scientist estimates that after a certain amount of time, there would be 25 33 105 bacteria in a Petri dish. About how many bacteria is this? 6. ACTIVISM A total of 54 73 people have signed a petition. How many people have signed the petition? 7. MEASUREMENT There are 106 millimeters in one kilometer. The distance from Dana’s house to her uncle’s house is 44 kilometers. What is this distance in millimeters? 8. DOGS Dedra’s dog weighs 5 24 pounds. What is the weight of Dedra’s dog? Problem-Solving Practice Powers and Exponents 083_102_HPC3C5_892764.indd 84 83_102_HPC3C5_892764.indd 84 2/2/10 10:02:01 PM /2/10 10:02:01 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 85 Course 2 5-1 Simplify. Express using exponents. 1. k8 · k 2. t7 · t6 3. 2w2 · 5w2 4. 3e3 · 7e3 5. 4r4 (-4r3 ) 6. (-3l 2 w3 )(2lw4 ) 7. (-11w4 )(-5w3 x4 ) 8. (-4b6 )(-b2 c3 ) 9. (10t4 v5 )(3t2 v5 ) 10. 59 − 53 11. 38 − 3 12. b6 − b4 13. g15 − g7 14. 18v5 − 9v 15. 24a6 − 6a5 16. y6 ÷ y3 17. n19 − n11 18. 9521 − 9518 19. Simplify 55 · 63 · 8 − 10 53 · 6 · 89 . 20. BONUSES A company has set aside 107 dollars for annual employee bonuses. If the company has 104 employees and the money is divided equally among them, how much will each employee receive? 21. CAR LOANS After making a down payment, Mr. Valle will make 62 monthly payments of 63 dollars each to pay for his new car. What is the total of the monthly payments? Get Connected Get Connected For more examples, go to glencoe.com. B Homework Practice Multiply and Divide Monomials 083_102_HPC3C5_892764.indd 85 83_102_HPC3C5_892764.indd 85 2/2/10 10:02:05 PM /2/10 10:02:05 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 86 Course 2 5-1 1. SOUND Decibels are units to measure sound. Ordinary conversation is rated at about 60 decibels (or a relative loudness of 106 ). Thunder is rated at about 120 decibels (or a relative loudness of 1012). How many times greater is the relative loudness of thunder than the relative loudness of ordinary conversation? 2. GEOMETRY Express the area of a square with sides of length 5ab as a monomial. 3. COMPUTERS The byte is the fundamental unit of computer processing. The byte is based on powers of 2, as shown in the table. How many times greater is a gigabyte than a megabyte? Memory Term Number of Bytes byte 20 or 1 kilobyte 210 megabyte 220 gigabyte 230 4. GEOMETRY The area of the rectangle in the figure is 24a2 b3 square units. Find the width of the rectangle. 5. BOOKS A publisher sells 106 copies of a new book. Each book has 102 pages. How many pages total are there in all of the books sold? Write the answer using exponents. 6. RABBITS Randall has 23 pairs of rabbits on his farm. Each pair of rabbits can be expected to produce 25 baby rabbits in a year. How many baby rabbits will there be on Randall’s farm each year? Write the answer using exponents. 6ab B Problem-Solving Practice Multiply and Divide Monomials 083_102_HPC3C5_892764.indd 86 83_102_HPC3C5_892764.indd 86 2/2/10 10:02:09 PM /2/10 10:02:09 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 87 Course 2 5-1 Simplify. 1. (6t5 ) 2 2. (4w9 ) 4 3. (12k6 ) 3 4. (15m8 )3 5. (4d3 e5 ) 7 6. (-4r6 s15)4 7. [(72 )2 ] 2 8. [(32 )2 ] 3 9. ( 3 − 5 a6 b9 ) 2 10. (4x2 ) 3 (3x6 ) 4 11. (0.6p5 ) 3 12. (1 − 5 w5 x3 ) 2 GEOMETRY Express the area of each square below as a monomial. 13. 9c6 d 14. 14g5 h9 15. MEASUREMENT In the Metric System, you would need to have (104 )2 grams to equal 1 metric ton. Simplify this measurement by multiplying the exponents, then simplify by finding the actual number of grams needed to equal 1 metric ton. 16. GAMING A video-game designer is using the expression 6n3 in a program to determine points earned, where n is the game level. Simplify the expression for the n2 level. Get Connected Get Connected For more examples, go to glencoe.com. C Homework Practice Powers of Monomials 083_102_HPC3C5_892764.indd 87 83_102_HPC3C5_892764.indd 87 2/2/10 10:02:13 PM /2/10 10:02:13 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 88 Course 2 5-1 1. DEBATE Charmaine and Aaron are having a debate. Charmaine thinks the answer to their math homework is (42 ) 4 , but Aaron says the answer is (44 ) 2 . Explain how both Charmaine and Aaron can be correct. 2. LAND Kate was given a square plot of land in which to build. If one side of the plot was (3a)3 feet long, express the area of her plot as a monomial. (3a) 3 3. CRAFTS Numa loves beads and wants to know which amount would be more, a thousand beads or (62 ) 3 beads? 4. TEST The teacher marked Silvano’s problem wrong on his test. (45 )4 = 49 Explain what he did wrong and give the correct answer. 5. WOOD Dmitry calculated that he needs 6s2 square inches of wood for each crate he makes. Simplify the expression when s is replaced by t4 . 6. VOLUME Express the volume of the following cube as a monomial. (4d) 2 C Problem-Solving Practice Powers of Monomials 083_102_HPC3C5_892764.indd 88 83_102_HPC3C5_892764.indd 88 2/2/10 10:02:16 PM /2/10 10:02:16 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 89 Course 2 5-1 Mixed Problem Solving For Exercises 1 and 2, use the act it out strategy. 1. BILLS Joaquin bought a DVD for $21. He gave the cashier two $20 bills. How many different combinations of $1, $5, and $10 bills can the cashier give him for change? 2. TENNIS Felix, Lolita, Tetsuo, Kaveri, and Maxine are on the school tennis team. When ranked from first to fifth, how many ways can they be ranked if Maxine is always first and Felix is always ranked above Tetsuo? Use any strategy to solve Exercises 3–6. Some strategies are shown below. PROBLEM-SOLVING STRATEGIES • Act it out. • Work backward. • Look for a pattern. • Choose an operation. 3. PUMPKINS Mr. Greene harvested pumpkins for selling at four markets. He sold one-fifth of his crop at the first market, 40 at the second, 25% of the remaining at the third, and twice what he sold at the second at the fourth market. If Mr. Greene has one pumpkin remaining, how many pumpkins did he sell? 4. CHORES Kimberley has the choice of washing the car, mowing the lawn, or raking leaves on Saturday and baking a cake, washing the dishes, or doing the laundry on Sunday. In how many ways can she choose one chore for each day? 5. FUNDRAISER The drama club is selling 100 T-shirts for $15 each for a fundraiser. The T-shirts cost a total of $623. If they sell all the T-shirts, how much money will be raised for the drama club? 6. NEWS Tuan told good news to two friends. They each told three friends, and each of their friends told three friends. How many people had heard good news at this point? Get Connected Get Connected For more examples, go to glencoe.com. D Homework Practice Problem-Solving Investigation: Act It Out 083_102_HPC3C5_892764.indd 89 83_102_HPC3C5_892764.indd 89 2/2/10 10:02:20 PM /2/10 10:02:20 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 90 Course 2 5-1 For Exercises 1–6, use the act it out strategy to solve. 1. PHOTOGRAPHY Maura has six photos that she has taken framed and hanging in a row on the wall. If she wants to rearrange them so that the middle two photos stay in place, how many different ways can she arrange the photos? 2. TEAMS There are 5 players on a basketball team. If Evan always plays in the point guard position, and Holman always plays in the power forward position, how many different ways can the coach arrange Mohe, Alki, and Shahid in the center, small forward, and off-guard positions? 3. MONEY Elaine wants to buy an apple that costs $0.55. How many different combinations of quarters, nickels, and dimes can be used to make $0.55? 4. AGES Parvin is older than Jan, who is older than Meg, who is older than Laurie, who is older than Vicky, who is older than Leslie. How many different ways can they stand in line so that the youngest person is always first, and the oldest person is always last? 5. E-MAILS Nina received two E-mails on Monday. Every day after that she received one more than twice as many as the day before. How many E-mails did she receive on Thursday? 6. MONEY Brian wants to buy a muffin that costs $0.80. How many different combinations of nickels and dimes can be used to make $0.80? D Problem-Solving Practice Problem-Solving Investigation: Act It Out 083_102_HPC3C5_892764.indd 90 83_102_HPC3C5_892764.indd 90 2/2/10 10:02:23 PM /2/10 10:02:23 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 91 Course 2 A Write each expression using a positive exponent. 1. 8−5 2. 3−9 3. z−2 4. p−4 Evaluate each expression. 5. (−6)−5 6. 8−4 7. 2−9 8. (−7)−3 Write each fraction as an expression using a negative exponent. 9. 1 − 29 10. − 1 64 11. 1 − e5 12. 1 − 74 Simplify. Express using positive exponents. 13. 65 − 62 14. n−2 · n−3 15. w3 − w−1 16. k−4 − k−6 17. ROADS A state highway that is 44 miles long runs parallel to a smaller country road that is 42 miles long. How many times longer than the country road is the state highway? Write the answer as a number with a positive exponent. 18. FUNDRAISERS The hospital spent 95 dollars on new medical equipment this year. Last year, they spent 97 dollars. How many times more money did they spend last year than this year? 19. MEASUREMENT 1 milligram is equal to 10−3 grams. Write this number using a positive exponent. 20. DISTANCE A long-distance runner runs 25 miles one week and 27 miles the next week. How many times farther did he run in the second week than in the first week? Get Connected Get Connected For more examples, go to glencoe.com. 5-2 Homework Practice Negative Exponents 083_102_HPC3C5_892764.indd 91 83_102_HPC3C5_892764.indd 91 2/2/10 10:02:26 PM /2/10 10:02:26 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 92 Course 2 A 1. MOTHS A Polyphemus Moth caterpillar weighs about − 1 642 times less when it first becomes a larva than it does when it is fully grown. Write this number using a negative exponent. 2. WEIGHT The length of one common termite is about 30−2 meters. Write this number using a positive exponent. 3. MONEY The school system spent 38 dollars on fuel for buses and school vehicles per week last year. This year, they spent 310 dollars per week. How many times more did they spend per week this year than last year? 4. MEASUREMENT The table converts the size of each measurement to kilograms. Write each number using a positive exponent. Amount Amount in Kilograms 1 centigram 10-5 1 decigram 10-4 1 dekagram 10-2 5. SCIENCE Electrons are smaller than 10-18 meters. Write this number using a positive exponent. 6. MONEY A bank loans a new business 67 dollars to get started. If the business pays back 65 dollars per year, how many years will it take to pay off the loan? Write your answer using a positive exponent. 5-2 Problem-Solving Practice Negative Exponents 083_102_HPC3C5_892764.indd 92 83_102_HPC3C5_892764.indd 92 2/2/10 10:02:30 PM /2/10 10:02:30 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 93 Course 2 Write each number in standard form. 1. 9.03 × 102 2. 7.89 × 103 3. 4.115 × 105 4. 3.201 × 106 5. 5.1 × 10-2 6. 7.7 × 10-5 7. 3.85 × 10-4 8. 1.04 × 10-3 Write each number in scientific notation. 9. 4,400 10. 75,000 11. 69,900,000 12. 575,000,000 13. 0.084 14. 0.0099 15. 0.000000515 16. 0.0000307 17. Which number is greater: 3.5 × 104 or 2.1 × 106 ? 18. Which number is less: 7.2 × 107 or 9.9 × 105 ? 19. POPULATION The table lists the populations of five countries. List the countries from least to greatest population. 20. SOLAR SYST EM Pluto is 3.67 × 109 miles from the Sun. Write this number in standard form. 21. MEASUREMENT One centimeter is equal to about 0.0000062 mile. Write this number in scientific notation. 22. DISASTERS In 2005, Hurricane Katrina caused over $125 billion in damage in the southern United States. Write $125 billion in scientific notation. Country Population Australia 2 × 107 Brazil 1.9 × 108 Egypt 7.7 × 107 Luxembourg 4.7 × 105 Singapore 4.4 × 106 Get Connected Get Connected For more examples, go to glencoe.com. 5-2 B Homework Practice Scientific Notation 083_102_HPC3C5_892764.indd 93 83_102_HPC3C5_892764.indd 93 2/2/10 10:02:33 PM /2/10 10:02:33 PM

NAME ________________________________________ DATE _____________ PERIOD _____ 1st pass Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 5 94 Course 2 1. MEASUREMENT There are about 25.4 millimeters in one inch. Write this number in scientific notation. 2. POPULATION In the year 2000, the population of Rahway, New Jersey, was 26,500. Write this number in scientific notation. 3. MEASUREMENT There are 5,280 feet in one mile. Write this number in scientific notation. 4. PHYSICS The speed of light is about 1.86 × 105 miles per second. Write this number in standard notation. 5. COMPUTERS A CD can store about 650,000,000 bytes of data. Write this number in scientific notation. 6. SPACE The diameter of the Sun is about 1.39 × 109 meters. Write this number in standard notation. 7. ECONOMICS The U.S. Gross Domestic Product in the year 2004 was 1.17 × 1013 dollars. Write this number in standard notation. 8. MASS The mass of planet Earth is about 5.98 × 1024 kilograms. Write this number in standard notation. 5-2 B Problem-Solving Practice Scientific Notation 083_102_HPC3C5_892764.indd 94 83_102_HPC3C5_892764.indd 94 2/2/10 10:02:37 PM /2/10 10:02:37 PM