เอกสารประกอบการเรียน เรื่อง ระบบสมการเชิงเส้นสองตัวแปร

MATHEMATICS

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ระบบสมการเชงิ เสน้

วิชาคณิตศาสตร์ 6 รหสั วิชา ค23102

ช่อื - สกลุ .....................................................................
ชน้ั ..................................เลขท.ี่ .......................................
ครผู สู้ อน นางสาวรมติ า ยพุ จันทร์

1

โรงเรียนสวนกหุ ลาบวิทยาลัย รงั สติ

เอกสารประกอบการเรียน
วิชาคณติ ศาสตร์ 5 ค23102 ชน้ั มัธยมศึกษาปีที่ 3 ภาคเรียนที่ 2

หนว่ ยท่ี 3 เรื่อง ระบบสมการเชิงเสน้
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ระบบสมการเชิงเส้นสองตัวแปร

ให้นกั เรยี นพิจารณาข้อความตอ่ ไปนี้
“ผลบวกของสองจำนวนนน้ั มีคา่ เป็น 9 และผลต่างของทง้ั สองจำนวนนัน้ เปน็ 3 จงหาจำนวนท้งั สอง
จำนวนนน้ั ”
จากข้อความดงั กล่าว กำหนดให้จำนวนหนึง่ เป็น x และอีกจำนวนหนึ่งเปน็ y จะเขยี นเป็นสมการดงั นี้

x + y = 9 ------ (1)
x – y = 3 ------ (2)
ระบบท่ปี ระกอบดว้ ยสมการ (1) และ (2) ขา้ งต้น เป็นตวั อยา่ งของ “ระบบสมการเชิงเส้นสองตัวแปร”

ให้ a , b , c , d , e และ f เปน็ จำนวนจริงท่ี a , b ไมเ่ ป็นศูนย์พรอ้ มกัน และ c , d ไมเ่ ป็นศนู ย์พรอ้ มกัน
ระบบที่ประกอบดว้ ยสมการ

ax + by = e
cx + dy = f
เรียกวา่ ระบบสมการเชิงเส้นสองตัวแปรที่มี x และ y เปน็ ตัวแปร
โดยท่ี a และ c เปน็ สมั ประสทิ ธขิ์ อง x
b และ d เป็นสมั ประสิทธิ์ของ y

คำตอบของระบบสมการเชงิ เสน้ สองตวั แปร คือ คู่อนั ดบั (x , y) ท่ีสอดคลอ้ งกบั สมการท้ังสองของระบบ
สมการ หรือ คู่อันดับ (x , y) เมื่อนำไปแทนคา่ ในสมการทงั้ สองแลว้ ทำใหร้ ะบบสมการนั้นเป็นจรงิ

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การหาคำตอบของระบบสมการเชงิ เสน้ สองตวั แปร

1. การหาคำตอบของระบบสมการเชิงเสน้ สองตวั แปรด้วยการเขียนกราฟ

ตัวอยา่ งท่ี 1 จงหาคำตอบของระบบสมการ โดยการเขียนกราฟของสมการทัง้ สองนี้
3x – y = 3 ------ (1)
2x + y = 2 ------ (2)

เขยี นกราฟของสมการทงั้ สองไดด้ ังน้ี

จากการเขยี นกราฟ จะเห็นวา่ กราฟทั้งสองตดั กนั ทัง้ หมด ......... จดุ ทจี่ ุด .......................
ซง่ึ จะได้วา่ คู่อนั ดับเพยี งค่เู ดยี ว คอื ................. เป็นคำตอบของระบบสมการ
สรุป ถ้ากราฟท้ังสองตัดกนั .................. จุด จะได้ว่า ระบบสมการนั้นมีคำตอบ .......................................................

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ตัวอยา่ งที่ 2 จงหาคำตอบของระบบสมการ โดยการเขียนกราฟของสมการทั้งสองน้ี
x – 2y = 1 ------ (1)
2x – 4y = 2 ------ (2)

เขยี นกราฟของสมการทั้งสองไดด้ งั น้ี

จากการเขียนกราฟ จะเหน็ วา่ กราฟทั้งสองตดั กันทงั้ หมด .........................................................จุด
หรือกราฟทงั้ สองมลี กั ษณะ.............................................. ซึง่ จะไดว้ ่า .....................................................................
สรปุ ถ้ากราฟทัง้ สองตัดกนั .......................................จะไดว้ ่า ระบบสมการนั้นมคี ำตอบ .........................................

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ตวั อย่างท่ี 3 จงหาคำตอบของระบบสมการ โดยการเขยี นกราฟของสมการทัง้ สองนี้
3x = 2y – 6 ------ (1)
2y – 3x = -3 ------ (2)

เขยี นกราฟของสมการท้งั สองได้ดังน้ี

จากการเขยี นกราฟ จะเหน็ ว่า กราฟทงั้ สอง .............................................................................................
ซง่ึ จะได้ว่า ระบบสมการนั้น ...................................................................................................................................

สรุป ถ้ากราฟท้ังสอง .............................................จะได้ว่า ระบบสมการนัน้ .......................................................

Concept. เมื่อนำสมการแตล่ ะสมการมาเขียนกราฟ จะสามารถอธิบายคำตอบจากลกั ษณะของกราฟได้ดังนี้
1. กราฟท้ังสองตัดกนั เพียงจุดเดียว จะได้วา่ ระบบสมการนนั้ มคี ำตอบเพียงคำตอบเดยี ว
2. กราฟทั้งสองทบั กันหรือเปน็ เสน้ ตรงเดียวกนั จะไดว้ า่ ระบบสมการน้ันมคี ำตอบมากมายไมจ่ ำกดั
3. กราฟทง้ั สองขนานกัน จะไดว้ ่าระบบสมการนนั้ ไม่มคี ำตอบของระบบสมการ

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แบบฝกึ หัด 3.1

1. จงเขยี นกราฟของระบบสมการตอ่ ไปน้ี แลว้ หาวา่ ระบบสมการตอ่ ไปน้มี คี ำตอบเดียว มหี ลายคำตอบ
หรือไมม่ คี ำตอบ
1) 2y – x = 6

2y = x – 4

ลกั ษณะคำตอบ .........................................................
2) x + y = 7

x–y=3

ลกั ษณะคำตอบ .........................................................

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3) y + x = -2
2y + 2x = -4

ลกั ษณะคำตอบ .........................................................
4) 2x – 3y – 14 = 0

3x + 2y = 8

ลกั ษณะคำตอบ ...........................................................

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2. จงพิจารณากราฟของระบบสมการต่อไปนว้ี า่ มีเพียงคำตอบเดียวหรอื ไม่

1) x + y = 3 กบั y = -x + 3 ...............................................................................................

2) 2y = x + 2 กับ y = 0.5x + 1 ...............................................................................................

3) x + 3y = 9 กับ 3y = -x + 9 ...............................................................................................

4) 4x + y = 1 กับ x – 2y = 7 ...............................................................................................

5) x + 2y = 3 กับ 2x + 4y = 6 ...............................................................................................

6) 2x – y = 1 กับ -4x + 2y = 5 ...............................................................................................

7) y = 3x + 1 กบั 9x – 3y = -3 ...............................................................................................

8) 25x – 5y = 1 กบั y = 5x ...............................................................................................

3. จงพิจารณากราฟของระบบสมการตอ่ ไปน้ีว่ามีคำตอบมากมายนับไมถ่ ้วนหรือไม่

1) 2x + 2y = 6 กบั y = -x + 3 ...............................................................................................

2) y = x + 2 กับ 3x = 3y – 6 ...............................................................................................

3) 2x + y = 9 กับ 2y = -4x + 7 ...............................................................................................

4) 4x + y = 1 กับ 3x – 2y = 9 ...............................................................................................

5) 5x + 2y + 5 = 0 กับ 2.5x + y = 2 .............................................................................................

6) -x – y = 1 กับ 2y = -2x – 2 ...............................................................................................

7) y = 6x + 1 กับ 18x – 3y = -3 ...............................................................................................

8) 7x – 3y = 1 กบั 14x = 6x + 2 ...............................................................................................

4. จงจบั คู่ระบบสมการท่ที ำใหร้ ะบบสมการน้นั ไม่มคี ำตอบ โดยนำอกั ษรท่อี ยูห่ นา้ สมการมาใสห่ น้าหมายเลขข้อ

...............1) y = 2x + 1 ก. -4x = -6y – 3

...............2) 3x = 6y – 5 ข. y = 0.5x

...............3) -4x + 4y = 3 ค. 2y = 8x + 5

...............4) 2y = 12x + 1 ง. 7x – 2y = -5

...............5) 3x – 2y = 0 จ. 2x + y = 5

...............6) 5y = 20x – 3 ฉ. 2y = 10x – 9

...............7) 15x – 3y – 12 = 0 ช. 6x – y = 7

...............8) y = 3.5x ซ. y = x – 4

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5. จงยกตัวอยา่ งระบบสมการ (ห้ามซำ้ กบั โจท์แบบฝึกหดั ) ท่ีมลี ักษณะคำตอบต่อไปน้ี
1) มีเพียงคำตอบเดียว ..........................................................................................................................
2) มีคำตอบมากมายไมจ่ ำกัด ...................................................................................................................
3) ไม่มีคำตอบของระบบสมการ ..............................................................................................................

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2. การหาคำตอบของระบบสมการโดยวธิ กี ารแทนคา่

การหาคำตอบของระบบสมการโดยวิธกี ารแทนคา่ สามารถทำได้ดังน้ี
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ตวั อย่างท่ี 1 จงหาคำตอบของระบบสมการตอ่ ไปน้ี

3x – y = 17
x + 2y = 8
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ตวั อยา่ งที่ 2 จงหาคำตอบของระบบสมการต่อไปน้ี
3x = 9 – 2y
x+y = 3
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ตัวอย่างท่ี 3 จงหาคำตอบของระบบสมการต่อไปน้ี
2x – y = -4
4x = 7 + 2y

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ตัวอย่างท่ี 4 จงหาคำตอบของระบบสมการตอ่ ไปนี้
x – 3y = 6
12 – 2x = -6y

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แบบฝกึ หัด 3.2

คำชี้แจง ใหน้ กั เรียนหาคำตอบของระบบสมการต่อไปน้โี ดยใชว้ ิธีการแทนค่า
1. x + 2y = 7

2x – y = 4
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2. x – 2y = 0

2x – y = 3
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3. 3y + 5x + 3 = 0

2x – 3y + 30 = 0
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4. 3y – x = 17
6y – 2x = 10

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5. 3y – 5x = -3

9y – 15x = -9
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6. 4(x + 3) = 3y + 7

2(y - 5) = x + 5
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7. m + 3n = 5
-2m + 5n = 1

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8. 5x – 6y = -4

3x + 2y = -8
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3. การหาคำตอบของระบบสมการโดยวิธกี ารกำจดั ตัวแปร
การหาคำตอบของระบบสมการโดยวิธกี ารกำจดั ตัวแปร สามารถทำไดด้ งั นี้
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ตวั อย่างท่ี 1 จงหาคำตอบของระบบสมการตอ่ ไปน้ีโดยวธิ ีการกำจดั ตัวแปร

2x + y = 1
2x – 3y = 13
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ตวั อยา่ งที่ 2 จงหาคำตอบของระบบสมการต่อไปนโ้ี ดยวธิ กี ารกำจดั ตวั แปร
3x + 2y = 4
2x – 3y = 7
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ตวั อย่างที่ 3 จงหาคำตอบของระบบสมการตอ่ ไปนโ้ี ดยวธิ ีการกำจัดตัวแปร

2x + 3y = 5

7x + 4y = 2

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ตัวอยา่ งท่ี 4 จงหาคำตอบของระบบสมการตอ่ ไปนีโ้ ดยวธิ ีการกำจดั ตัวแปร

3 x − 3 y = 145
2 4
4 5
3 x − 3 y = 3

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ตวั อยา่ งที่ 5 จงหาคำตอบของระบบสมการต่อไปนโี้ ดยวิธกี ารกำจดั ตัวแปร

3x − 2y = y – 5x
4

2y – 23x = 5

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ตวั อยา่ งที่ 6 จงหาคำตอบของระบบสมการตอ่ ไปน้ีโดยวิธีการกำจดั ตวั แปร

y − 2x = 4x − 2y
5 3
x+2 1−y
3 = 9

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แบบฝึกหดั 3.3

คำช้ีแจง ใหน้ ักเรยี นหาคำตอบของระบบสมการต่อไปนโี้ ดยวธิ ีการกำจดั ตัวแปร
1. x + 2y = 12

X – 2y = 4
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2. -2x + 3y = 12

2x + 5y = 36
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3. q – 6 = 2(p + 3)

q + 2 = -3(p + 2)
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4. 0.03x + 0.2y = 0.07

0.04x + 0.5y = 0.21

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5. 2(u + 3) + (v - 1) = 6

-(u + 3) + 4(v - 1) = 15

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6. 1 x + 1 y = 2
2 3 3
1 1 7
3 x + 5 y = 15

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7. 1 − 1 = 1
3x 4y 4
1 1
3x − 2y = 1

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8. จงหาค่า a ท่ที ำให้ระบบสมการนมี้ ีคำตอบเป็น (1 , -4)
6x – y = 10
-2x + ay = 6

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9. จงหาค่า k ท่ีทำให้ระบบสมการนม้ี คี ำตอบมากมายไม่จำกดั

2x – 3y = 8
5x + ky = 20
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10. จงหาค่า m ทที่ ำใหร้ ะบบสมการน้ีไมม่ ีคำตอบ

5x – y = 20

2x + my = 14

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11. ถา้ (a , b) เป็นคำตอบของระบบสมการ

0.03x + 0.1y = 0.02

0.02x + 0.3y = 0.2

แล้ว ab มคี ่าเทา่ ใด

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21

4. โจทยป์ ญั หาระบบสมการเชงิ เสน้ สองตวั แปร

4.1 โจทยป์ ัญหาเกี่ยวกบั ปญั หาทางคณติ ศาสตร์

ตัวอย่างที่ 1 ถา้ คร่ึงหนึ่งของผลบวกของจำนวนสองจำนวนเปน็ 43 และสามเทา่ ของจำนวนน้อย มากกว่าสองเท่าของ
จำนวนมากอยู่ 23 จงหาสองจำนวนนนั้
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ตัวอยา่ งท่ี 2 เส้นรอบรปู ของรปู สเ่ี หลี่ยมผนื ผ้ารูปหนง่ึ เท่ากับ 10 ฟุต ถา้ สองเท่าของความยาวด้านกวา้ งเทา่ กับ
คร่งึ หน่งึ ของความยาวดา้ นยาว จงหาพนื้ ที่ของรปู สีเ่ หลย่ี มผืนผา้ รูปนี้
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22

ตวั อย่างที่ 3 เมื่อสิบปีท่แี ลว้ ออฟมีอายุน้อยกวา่ เอฟ 18 ปี ปัจจบุ นั อายุของทงั้ สองคนรวมกันได้ 100 ปี ถา้ ถัด
จากปีปัจจุบนั ไปอีก 5 ปี เอฟจะมีอายุเทา่ ใด
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23

แบบฝึกหัด 3.4

คำชแ้ี จง จงแสดงวธิ หี าคำตอบของโจทย์ปญั หาต่อไปน้ี
1. จำนวนจำนวนหนงึ่ มากกว่าครึ่งหนง่ึ ของจำนวนอกี จำนวนหนงึ่ อยู่ 4 ผลต่างของจำนวนท้ังสองน้เี ท่ากับ 2 จงหา
จำนวนสองจำนวนน้ี
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2. ความยาวเส้นรอบรูปของรูปสามเหลี่ยมหน้าจั่วเทา่ กบั 32 น้ิว ถ้าความยาวของดา้ นฐานมากกวา่ ครึ่งหน่งึ ของ
ความยาวด้านคู่ท่ยี าวเท่ากนั อยู่ 2 น้วิ จงหาความยาวแตล่ ะดา้ นของรปู สามเหลยี่ มหน้าจว่ั นี้
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3. ผลรวมอายุพหี่ นอ่ ยและน้องนอ้ ยเท่ากับ 26 ปี ผลตา่ งระหว่างส่เี ทา่ ของอายุพห่ี น่อยและสองเท่าของอายุน้องนอ้ ย
เท่ากบั 28 ปี จงหาอายขุ องพ่หี นอ่ ยและน้องนอ้ ย
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24

4. จำนวนที่มสี องหลกั จำนวนหนึ่ง มคี ่ามากกว่าผลบวกของเลขโดดในแตล่ ะหลักอยู่ 9 และจำนวนที่มเี ลขโดด
สลบั หลักกันจะมีค่าน้อยกว่าสีเ่ ท่าของจำนวนเดิมอยู่ 3 จงหาจำนวนจำนวนน้ี
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25

4.2 โจทย์ปัญหาเกี่ยวกบั แรงงาน

ตัวอยา่ งท่ี 4 ภพและนวตั ชว่ ยกนั ทำงานอย่างหนง่ึ จนงานเสร็จ ใชเ้ วลาท้ังสิ้น 28 ชว่ั โมง ถ้าภพทำงานนค้ี นเดียว
เป็นเวลา 8 ชว่ั โมง แล้วจงึ ใหน้ วัตมาทำงานนต้ี ่ออีก 63 ช่วั โมง งานจงึ จะเสรจ็ จงหาว่าถ้าให้แตล่ ะคนทำงานนี้
คนเดียวงานจะเสรจ็ ในเวลากี่ช่วั โมง
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ตัวอย่างท่ี 5 ผ้ชู าย 3 คน กบั ผหู้ ญิง 4 คน ทาสีตึกหลงั หนึ่งเสรจ็ ใน 14 วัน และผูช้ าย 10 คน กับผู้หญงิ 15 คน
ทาสีตึกแบบเดยี วกนั และขนาดเท่ากนั กับกลุ่มแรก เสรจ็ ใน 4 วนั ถา้ ผู้ชาย 7 คนกับผู้หญงิ 6 คนทาสีตึกแบบเดียวกัน
และขนาดเท่ากันกบั ท้งั สองกล่มุ จะเสร็จในเวลากี่วัน
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26

ตวั อย่างท่ี 6 เด็ก 3 คน กบั ผู้ใหญ่ 8 คน ทำงานอยา่ งหนง่ึ เสรจ็ ในเวลา 10 วนั และเดก็ 10 คน กับผูใ้ หญ่ 15 คน
ทำงานอยา่ งเดียวกนั น้ี จะแล้วเสร็จในเวลา 4 วนั จงหาวา่ ถ้าเด็ก 5 คน กับผใู้ หญ่ 4 คน ทำงานเดียวกันน้จี ะเสรจ็
ในเวลากี่วัน
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27

แบบฝกึ หดั 3.5

คำช้แี จง จงแสดงวิธหี าคำตอบของโจทย์ปญั หาตอ่ ไปนี้
1. ชาย 4 คน หญิง 5 คน ชว่ ยกนั ทำงานชิ้นแล้วเสร็จในเวลา 8 วัน แต่ถา้ ชาย 6 คน หญิง 10 คน ช่วยกนั ทำงาน
ชน้ิ เดยี วกันนี้จะแลว้ เสร็จในเวลา 5 วนั จงหาว่า ถ้าหญิง 3 คน กับชาย 5 คน ช่วยกนั ทำงานชิน้ เดยี วกันนี้จะแลว้
เสร็จในเวลากีว่ ัน
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2. เด็ก 2 คน กบั ผู้ใหญ่ 5 คน ขุดบ่อเสรจ็ ใน 4 วัน ถ้าเด็ก 3 คน กบั ผู้ใหญ่ 4 คนจะขุดบ่อนเี้ สรจ็ ใน 3 วัน

ดังนน้ั ถ้าใหเ้ ด็ก 3 คน จะขดุ บ่อนีเ้ สร็จในเวลากีว่ ัน

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28

3. ชาย 2 คน กับหญงิ 5 คน ช่วยกันปกู ระเบื้องพ้นื โรงงานแห่งหนงึ่ เสร็จในเวลา 4 วัน แต่ถ้าให้ชาย 3 คน
กับหญิง 4 คน ปูกระเบอ้ื งโดยใชก้ ระเบ้อื งขนาดเดียวกันและปริมาณงานเทา่ กันกับกลุ่มแรก จะเสร็จในเวลา 3 วนั
จงหาว่าถา้ ให้ผ้ชู ายคนเดยี วปูกระเบ้ืองจะเสรจ็ ในเวลากวี่ นั
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29

4.3 โจทยป์ ญั หาเกี่ยวกับของผสม

ตัวอยา่ งท่ี 7 ซอื้ สม้ มาสองชนิดราคา 30 บาท และ 40 บาท นำมาคละกนั แลว้ ขายไปในกิโลกรัมละ 35 บาท
ได้เงินเท่าทนุ พอดี จงหาอตั ราส่วนของการผสมของส้มท้ังสองชนดิ
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ตัวอย่างที่ 8 ผสมแป้งสาลีชนิดหนึ่งราคากิโลกรัมละ 4 บาท กับแปง้ มันชนดิ ราคากิโลกรมั ละ 5.50 บาท จงหาวา่
จะต้องใช้อัตราส่วนผสมของแป้งสาลีตอ่ แป้งมันโดยนำ้ หนกั เปน็ เท่าไร จึงจะขายแป้งผสมในราคากโิ ลกรมั ละ 6 บาท
แล้วยงั ไดก้ ำไร 20%
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30

ตัวอยา่ งท่ี 9 มีนำ้ เช่อื มเข้มขน้ อยู่ 2 ชนดิ ชนดิ A มนี ้ำตาล 30% ชนดิ B มีน้ำตาล 20% ถ้าตอ้ งการนำนำ้ เชือ่ ม
มาผสมกันใหม้ ีความเข้มข้นของน้ำตาล 25% จำนวน 800 ลกู บาศก์เซนตเิ มตร จะต้องใชน้ ้ำเชื่อมแต่ละชนิดปรมิ าณ
เทา่ ใด
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31

แบบฝกึ หัด 3.6

คำชี้แจง จงแสดงวธิ ีหาคำตอบของโจทย์ปญั หาต่อไปน้ี
1. ซอ้ื ข้าวสารหอมมะลิแดงกิโลกรมั ละ35 บาท และมะลิพนั ธุ์105 ราคากิโลกรัมละ 45 บาท คิดเป็นเงนิ 550 บาท
เม่ือนำมาผสมกันแล้วขายไปกิโลกรมั ละ 50 บาท ไดเ้ งนิ 700 บาท จงหาว่าซือ้ ข้าวสารมะลิแดง และข้าวสารมะลิพนั ธุ์
105 มาอย่างละกก่ี โิ ลกรมั
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2. ซื้อนำ้ ตาลทรายสองชนดิ ราคากโิ ลกรมั ละ 18 บาท และ 25 บาท นำมาผสมกันแล้วขายกิโลกรัมละ 24 บาท
ได้กำไร 20% จงหาอตั ราส่วนของการผสม
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3. สารชนิดหนึง่ มีแอลกอฮอล์ 12% สารชนดิ ที่สองมีแอลกอฮอล์ 60% ถา้ นำสารทัง้ สองชนิดมาผสมกันจะได้
สารผสมทม่ี ีแอลกอฮอล์ 24% และมปี รมิ าตร 32 ลติ ร จงหาว่านำสารทัง้ สองมาผสมอย่างละกีล่ ิตร
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4.4 โจทยป์ ัญหาเก่ยี วกับกระแสลมและกระแสน้ำ

อตั ราเร็วเรือตามน้ำ = อตั ราเร็วเรือในนำ้ นงิ่ + อตั ราเร็วของกระแสนำ้
อตั ราเรว็ เรอื ทวนนำ้ = อัตราเร็วเรือในนำ้ นิ่ง – อัตราเรว็ ของกระแสน้ำ

ตัวอยา่ งที่ 10 เรือลำหนึ่งแล่นตามนำ้ ไดร้ ะยะทาง 20 กิโลเมตร ในเวลา 50 นาที ถ้าแล่นทวนนำ้ จะไดร้ ะยะทาง
15 กิโลเมตร ในเวลา 45 นาที จงหาอตั ราเร็วของเรอื ในน้ำนิง่ และอัตราเรว็ ของกระแสน้ำ
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ตัวอยา่ งที่ 11 ในเวลา 5 ช่ัวโมง เครื่องบิน บนิ ตามลมไดร้ ะยะทาง 4,000 กโิ ลเมตรในเวลา 5 ชั่วโมง แต่บนิ
ทวนลมไดร้ ะยะทาง 3,000 กิโลเมตร จงหาอตั ราเรว็ ของเคร่ืองบินลำนีเ้ ม่ืลมสงบและอตั ราเรว็ ของกระแสลม
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34

แบบฝึกหดั 3.7

คำชแี้ จง จงแสดงวิธีหาคำตอบของโจทย์ปัญหาตอ่ ไปนี้
1. กอลลัมพายเรือในนำ้ นิง่ ได้ชว่ั โมงละ 20 กโิ ลเมตร แตถ่ ้าพายเรือทวนนำ้ จะไดร้ ะยะทาง 5 กิโลเมตร โดยใช้เวลา
20 นาที จงอัตราเร็วของกระแสน้ำ
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2. น้องดอกไม้พายเรอื ตามนำ้ ได้ระยะทาง 20 กิโลเมตร ใช้เวลา 2 ชว่ั โมง แต่ถ้าพายเรือทวนน้ำในระยะทางเทา่ เดมิ
จะใชเ้ วลา 2 ชวั่ โมง 30 นาที จงหาอตั ราเรว็ ของการพายเรือในน้ำนิ่งของน้องดอกไม้
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