ASVAB How To Solve Percent Word Problems

HOW TO SOLVE PERCENT PROBLEMS ON THE ASVAB TEST

2014

HOW TO SOLVE
PERCENT PROBLEMS
ON THE ASVAB TEST

Explanation, Examples and Practice Problems

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1/1/2014

HOW TO SOLVE PERCENT PROBLEMS ON THE ASVAB TEST

When answering a question that involves percentages, the trick is to translate it into an equation.
Substitute either 0.01 or
for the percent sign, and let x (or any variable you like) stand for the number you’re trying to find. Then
use algebra to solve for x. Translate the word percent or symbol to .01; translate is to =; and
translate of to multiplication sign
Here are two examples of practice problems you may see on the ACT.
Example 1
What percent of 600 is 270?

A good way to solve this type of percent problem is to translate the words into an equation. Here’s how
the example problem would look:
Substitute 0.01 for the percent sign in this equation and solve for x:

Thus, 45 percent of 600 is 270, so the correct answer is Choice (C).

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HOW TO SOLVE PERCENT PROBLEMS ON THE ASVAB TEST

Example 2
If 40 percent of a is 30, then a is what percent of 50?

To answer this question, you first need to find the value of a, so make an equation from the values in the
first part of the question. Here’s how it would look:
Now solve this equation for a:

Thus, a = 75. Finally, you make an equation from the values in the second part of the question. Here’s
how: “75 is what percent of 50” becomes
Substitute 0.01 for the percent sign in this equation and solve for x:

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HOW TO SOLVE PERCENT PROBLEMS ON THE ASVAB TEST

So the correct answer is Choice (K).
Many students find math questions that involve percent increase and percent decrease confusing. The
first step to know when percent is an increase or a decrease.
Some common scenarios for percent increase questions are

• Sales tax added to the price of an item
• Tipping a server at a restaurant
• Interest earned on an investment
Some typical situations for percent decrease questions are
• Money lost on an investment
• Discount on an item being sold
• Deduction from a paycheck due to taxes
After you know whether you’re dealing with percent increase or percent decrease, here’s how you handle
the calculations:
• Increase. Calculate a percent increase as 100 percent (or 1) + the percent( number • .01). For

example, a percent increase of 15 percent is equal to
or 1.15

• Decrease. Calculate a percent decrease as 100 percent (or 1) – the percent( number • .01) . For
example, calculate a percent decrease of 20 percent as
or .8

The following two examples show you how to handle both types of questions from start to finish.
Example 1
Randy bought a small guitar amplifier priced at $165 with a special coupon that gave him a 15-percent
discount. About how much did he end up paying for the amp?
(A) Less than $100
(B) Between $100 and $120
(C) Between $120 and $140
(D) Between $140 and $160
(E) More than $160

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HOW TO SOLVE PERCENT PROBLEMS ON THE ASVAB TEST

A 15-percent discount is a percent decrease of 15 percent:
Use your calculator to find this percentage of the original price of $165:
Thus, the correct answer is Choice (D).
You can apply this method for finding percent increase and decrease to many percent problems.
Example 2
Keith’s portfolio is currently worth $10,200, representing a 20-percent increase on his original investment.
How much did he originally invest?
(F) $7,800
(G) $8,160
(H) $8,440
(J) $8,500
(K) $8,880
A 20-percent increase is calculated as
so use the following formula:

Change the percent sign to 0.01 and solve:

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HOW TO SOLVE PERCENT PROBLEMS ON THE ASVAB TEST

Alison’s salary was $40,000 last year, and at the end of the year she received a 5%
raise. What will she earn this year?
How to solve:

1.) Realize that Alison got a raise
2.) So whatever she makes this year, it will be more than she made last year.
The key to setting up this type of problem is to think of percent increase
• “100% of last year’s salary plus 5% of last year’s salary.” Here’s the word
equation:
This year’s salary = 100% of last year’s salary + 5% of last year’s salary
This year’s salary = (100% + 5%) of last year’s salary = 105% of last year’s salary
Change the percent to a (.01) times 105 and the word of to a multiplication sign; then
fill in the amount of last year’s salary:
This year’s salary = 1.05 $40,000
Now you’re ready to multiply:
This year’s salary = $42,000
So Alison’s new salary is $42,000

Now let’s do some practice problems,

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HOW TO SOLVE PERCENT PROBLEMS ON THE ASVAB TEST

A shirt originally cost $20, but during a sale its price was reduced by 15%.
What is the current price of the shirt?

A. $3
B. $5
C. $13
D. $17
E. $23

The original price of a banana in a store is $2. During a sale, the store
reduces the price by 25% and Joe buys the banana. Joe then meets his
friend, Sam, who is almost faint with hunger. Seeing an opportunity, Joe
raises the price of the banana 10% from the price at which he bought it, and
sells it to Sam. How much does Sam pay?

Check the answer and explanation page to see if you are right.

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HOW TO SOLVE PERCENT PROBLEMS ON THE ASVAB TEST

Answer and Explanation

A shirt originally cost $20, but during a sale its price was reduced by 15%.
What is the current price of the shirt?

Write what is given

• Original price: $20 * Original = start or beginning price
• 15% * 15 x .01 = .15
• Reduce= less or subtract

Write equation

Start $20 x .15 (percent) = $3.00

$3.00 = amount reduced

Start price – amount reduced = sale or current price
$20 - $2 = $17.00 Answer (d)

The original price of a banana in a store is $2. During a sale, the store
reduces the price by 25% and Joe buys the banana. Joe then meets his
friend, Sam, who is almost faint with hunger. Seeing an opportunity, Joe
raises the price of the banana 10% from the price at which he bought it, and
sells it to Sam. How much does Sam pay?

Write what is given

Original price $2 25% = 25 x .01 = .25 Reduced = subtract

Write equation

$2.00 x .25 = $.50 Original x percent= discount

$2.00 - $.50 = $1.50 Original – discount = new price or reduced price

Original price $1.50 10% = 10 x .01 = .10 Raise = add

$1.50 + .10 = $1.60 Original price + increase = new price or raised price

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