Joint and Combined Variations

1. Which of the following is the equation of variation where c varies jointly as g and f and c=24 when g=2 and f=3.

• A. K = cgf

• B. C=kgf

• C. G = kcf

• D. F=kcg

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CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

2. Which of the following situations illustrates combined variations?

• A) A varies directly as B and inversely as C

• B) B varies jointly as D and inversely as M

• C) P is directly proportional to Q and inversely proportional to R

• D) All of the above

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CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

For numbers 3-4, refer to the given problem.

The cost (C) of labor varies jointly as the number of workers (W) and the number of days (D) they work. If 10 men working 8 days each are paid Php560,

3. Which of the following is the value of the variation constant?

• A. 3

• B. 5

• C. 7

• D. 9

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CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.4

4. The cost (C) of labor varies jointly as the number of workers (W) and the number of days (D) they work. If 10 men working 8 days each are paid Php560. How many days will it take 12 men to earn Php756?

• A. 5

• B. 7

• C. 9

• D. 11

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CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.4

5. T varies directly as the square of P and inversely as Z. Using k as the constant of variation, which of the following is the equation of variation?

• A. T = kp² / z

• B. T = kpz²

• C. T = kz² / p

• D. T = pz² / k

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

6. T varies directly as the square of P and inversely as Z and T=12 when P=3 and Z=6, Which of the following is the value of the variation constant?

• A. 6

• B. 8

• C. 10

• D. 12

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CCSS.HSA.CED.A.1

7. T varies directly as the square of P and inversely as Z and T=12 when P=3 and Z=6, Which of the following is twice the value of T when P=9 and Z=6?

• A. 108

• B. 216

• C. 54

• D. 36

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.REI.A.1

8. Z varies jointly as Y and W and inversely as the square of X. if Z=360, y=24, w=20 and x=4, which of the following is the value of the variation constant?

• A. 12

• B. 15

• C. 18

• D. 21

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.4

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.B.3

9. Z varies jointly as Y and W and inversely as the square of X. if Z=360, y=24, w=20 and x=4, Which of the following is the variation equation of the problem?

• A. Z = yw / x²

• 
• 
• 

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CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.2

10. Z varies jointly as Y and W and inversely as the square of X. if Z=360, y=24, w=20 and x=4 , Which of the following is half the value of Z when y=27, w=15 and x=3?

• A. 540

• B. 360

• C. 270

• D. 180

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.4

CCSS.HSA.REI.A.1