Name________________________________________________
Direct vs. Inverse Variations
Date_________
IA1 Per_______
1. If y varies directly as x and y = 36 when x = 2, find x when y = 72.
2. If x varies inversely as y and x = 16 when y = 6, what is the value of y when x = 3?
3. A company that sells digital cameras has found the number of cameras it can sell is inversely proportional to the price
of the computer. Eighty cameras can be sold when the price is $250. Approximately how many cameras can be sold
when the price is $225?
4. The amount of medication prescribed for a person varies directly with the person’s weight. When a person weighs 65
kg, 4 ml of medication are prescribed. How many milliliters of medication should be prescribed to a person who weighs
85 kg?
5. Distance traveled varies directly as the time (t) required to travel that distance. If a car can travel 60 miles in 1.5
hours, find what distance was traveled in 4 hours.
6. A part-time workers weekly wages are directly related to how many hours they work. Michelle, a part-time
employee, worked 15 (h) last week and her wages totaled $105 (w). This week, Michelle will be working 27 hours. What
will her total wages be?
7. If x varies inversely as y and x measures 14 when y is 6, find x when y is 4.
8. The quantities p and q vary inversely. If p = 20 when q = -2, and p = x when q = -2x + 2, what is the value of x?
9. If x varies inversely as y and x = 12 when y = 3, what is the value of x when y = 9?
10. Boyle's Law states that the pressure of compressed gas is inversely proportional to its volume. The pressure
of a certain sample of a gas is 16 kilopascals when its volume is 1,800 liters. What is the pressure, in kilopascals,
when its volume is 900 liters?
11. A pulley that has a diameter of 8 inches is belted to a pulley that has a diameter of 12 inches. The 8-inchdiameter pulley is running at 1,548 revolutions per minute. If the speeds of the pulleys vary inversely to their
diameters, how many revolutions per minute does the larger pulley make?
12. The amount of money each member of a band earns playing at a graduation party varies inversely as the
number of members in the band. If the band has five members, each member earns $70.
a) Write an equation that models the relationship between the number of members in a band, n, and the
amount each member earns, d.
b) Use the equation to calculate the amount each member earns if there are four members in the band.
13. The speed of a gear varies inversely as the number of teeth it has. If a gear with 24 teeth rotates at a speed
of 45 revolutions per minute, how many revolutions per minute will a gear with 36 teeth make?
14. The number of calories burned while jogging varies directly with the number of minutes spent jogging. If
George burns 150 calories by jogging for 20 minutes, how many calories does he burn by jogging for 30 minutes?
15. Julio’s wages vary directly as the number of hours that he works. If his wages for 5 hours are $29.75, how
much will he earn for 30 hours?