5.1 - Variation Practice

≈462

For a fixed number of miles, the gas mileage of a car (mi/gal) varies inversely with the number of gallons used. One year an employee driving a truck averaged 24 miles per gallon and used 750 gallons of gas. If the next year, to drive the same number of miles the employee drove a compact car averaging 39 miles per gallon, how many gallons of gas would be used?

7

If a varies directly with b, and a = 15 while b = 5...what does b equal when a = 21?

-25/7

If a varies inversely with b, and a = 15 while b = -5...what does b equal when a = 21?

60

If m varies directly with n, and m = 30 while n = 6...what does m equal when n = 12?

15

If m varies inversely with n, and m = 30 while n = 6...what does m equal when n = 12?

80

If s varies directly with r, and s = 14 while r = 7...what does s equal when r = 40?

49/20

If s varies inversely with r, and s = 14 while r = 7...what does s equal when r = 40?

$90

Janet received $55.35 in interest on the $1230 in her credit union account. If the interest varies directly with the amount deposited, how much would Janet receive for the same amount of time if she had $2000 in the account?

$47.50

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

$612.50

The cost c of materials for a deck varies jointly with the width w and the length l. If c = $470.40 when w = 12 and l = 16 , find the cost when w = 10 and l = 25.

576

The strength of a rectangular beam varies jointly as its width and the square of it depth. If the strength of a beam three inches wide by 10 inches deep is 1200 pounds per square inch, what is the strength of a beam 4 inches wide and 6 inches deep?

7.5

The time needed to paint a fence varies directly with the length of the fence and indirectly with the number of painters. If it takes 5 hours to paint 200 feet of fence with 3 painters, how long will it take 5 painters to paint 500 feet of fence?

4.8

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?

4.2

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?

8

The time to prepare a field for planting varies inversely to number of people who are working. A large field can be prepared by 5 workers in 24 days. In order to finish the field sooner, the farmer plans to hire additional workers. How many workers are needed to finish the field in 15 days?

$437,202

The value of real estate V varies jointly with the neighborhood index N and the square footage of the house S. If V = $376, 320 when N = 96 and S = 1600 , find the value of a property with N = 83 and S = 2150 .

12

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

20.25

To build a sound wall along the highway, the amount of time t needed varies directly with the number of cement blocks c needed and inversely with the number of workers w. A sound wall made of 2400 blocks, using six workers takes 18 hours to complete. How long would it take to build a wall of 4500 blocks with 10 workers?

$8.75

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 with 250 vitamins cost?

2.5

An egg is dropped from the roof of a building. The distance it falls varies directly with the square of the time it falls. If it takes ½ second for the egg to fall eight feet, how long will it take the egg to fall 200 feet?

15/2

If w varies directly with b, and w = 5 while b = 10...what does w equal when b = 15?

≈162.6

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?

≈318

The number of gallons g in a circular swimming pool varies jointly with the square of the radius r² and the depth d. If g = 754 when r = 4 and d = 2 , find the number of gallons in the pool when r = 3 and d = 1.5 .

17.8

The number of gallons g of fuel used on a trip varies directly with the number of miles m traveled. If a trip of 270 miles required 12 gallons of fuel, how many gallons are required for a trip of 400 miles?

75

The number of revolutions made by a tire traveling over a fixed distance varies inversely to the radius of the tire. A 12 inch radius tire makes 100 revolutions to travel a certain distance. How many revolutions would a 16 inch radius tire require to travel the same distance?