Direct and inverse variation word problems

The volume V of a gas kept at a constant - temperature varies inversely with the pressure p. If the pressure is 24 pounds per square inch, the volume is 15 cubic feet. What type of variation problem is this and which is the formula?

• Direct; $V=k\cdot p$

• Direct; $p=k\cdot V$

• Inverse; $V=\frac{k}{p}$

• Inverse; $p=\frac{k}{V}$

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CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

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CCSS.HSF.LE.A.2

The volume V of a gas kept at a constant - temperature varies inversely with the pressure p. If the pressure is 24 pounds per square inch, the volume is 15 cubic feet. What will the volume be when the pressure is 30 pounds per square inch?

• k=360

• V=12

• V=18.75

• V=24

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

The amount of money spent at the gas station varies directly with the number of gallons purchased. When 11.5 gallons of gas were purchased the cost was $37.72. Write the equation?

•  $37.72=k\cdot11.5$  

•  $m=3.28\cdot g$  

•  $37.72=\frac{k}{11.5}$  

•  $m=\frac{433.78}{g}$  

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CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.2

The amount of money spent at the gas station varies directly with the number of gallons purchased. When 11.5 gallons of gas were purchased the cost was $37.72. How much would 8 gallons of gas cost?

• m=$22.60

• m=$30

• m=$54.22

• m=$26.24

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

The time to complete a project varies inversely with the number of employees. If 3 people can complete the project in 7 days, how long will it take 5 people? 

• t=4.2 days

• t=5 days

• t=21 days

• t=3 days

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.REI.B.3

The time needed to travel a certain distance varies inversely with the rate of speed. If it takes 8 hours to travel a certain distance at 36 miles per hour, how long will it take to travel the same distance at 60 miles per hour?  hint: use  $t=\frac{k}{s}$  

• s =4.8 hours

• t=4.8 hours

• s=13.33 hours

• t=13.33 hours

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CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.4

The number of centimeters y in a linear measurement varies directly with the number of inches x in the measurement. Pablo's height is 152.4 centimeters or 60 inches. What is Maria's height in centimeters if she is 64 inches tall?

• Maria is 162.56 cm

• Maria is 160.30 cm

• Maria is 145.6 cm

• Maria 156.8 cm

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CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.2

The number of revolutions made by a tire traveling over a fixed distance varies inversely with the radius of the tire. What variation formula should be used to find k?

• $revolutions=k\cdot radius$

• $radius=k\cdot revolutions$

• $revolutions=\frac{k}{radius}$

• $radius=\frac{k}{revolutions}$

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CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

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Karen earns $28.50 for working 6 hours. If the amount m she earns varies with h the number of hours she works, how much will she earn for working 10 hours?

• m=4.75

• m=47.50

• m=17.10

• m=171

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CCSS.HSF-LE.A.1B

A bottle of 150 vitamins costs $5.25. If the cost varies directly with the number of vitamins in the bottle, what should a bottle of 250 vitamins cost?

• c=10.75

• c=9.75

• c=7.25

• c=8.75

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CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.REI.B.3