Inverse Variation
Name: ____________________
Math 2
Spring 2014
Given that y varies inversely with x, use the specified values to write an inverse variation equation
that relates x to y.
1.
2.
3.
4.
5. y varies inversely with x. If y = 40 when x = 8, find x when y = 10.
6. y varies inversely with x. If y = 10 when x = -4, find y when x = 5.
7. a varies inversely as z. If a = ¼ when z = 6, find z when a = 9.
8. a varies inversely with b. If a = -25 when b = 1, find a when b = -6.
Identify whether each situation can be modeled by direct variation, inverse variation, or neither.
9. Fred earns $6.50 per hour. _________________
10. Edwina earns $450 plus 7.5% commission on sales. ________________
11. A car travels 250 miles to Myrtle Beach; the faster the car goes, the less time the trip takes.
___________________
12. For his flooring business, Joe needs to convert feet to yards. _______________
13. The volume of water in a swimming pool as it is filed at a rate of 200 gallons per minute. _________
14. If the area of a rectangle remains constant and the width decreases, then the length increases
____________________
15. You purchase a new SUV, the resale price decreases _________________
Answer each of the following questions. Some are models of direct variation, some are models of
inverse variation.
16.The electric current I, is amperes, in a circuit varies directly as the voltage V. When 12 volts are
applied, the current is 4 amperes. What is the current when 18 volts are applied?
17. The number of kilograms of water in a person’s body varies directly as the person’s mass. A
person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a
person with a mass of 150 kg?
18. The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If
the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?
19. The owner of an electronics store determines that the monthly demand for a computer varies
inversely with the price of the computer. When the price is $700, the monthly demand is 250
units. What is the monthly demand when the price is $500?
20. Your distance from lightning varies directly with the time it takes you to hear thunder. If
you hear thunder 10 seconds after you see the lightning, you are about 2 miles from the
lightning.
a. Write a direct variation equation for the relationship between time and distance.
b. Estimate how many seconds it would take for the thunder to travel a distance of 4
miles.
21. For the Choir fundraiser, the number of tickets Allie can buy is inversely proportional to the price
of the tickets. She can afford 15 tickets that cost $5 each. How many tickets can Allie buy if each cost
$3?
22. The time it takes you to get to campus varies inversely as your driving speed. Averaging 20 miles per
hour in bad traffic, it takes you 1.5 hours to get to campus. How long would the trip take averaging 50
miles per hour?