Name:_________________________________________
Period:________
IP#5-10: Direct and Inverse Variation
In your group, take the direct/inverse variation cards and sort them according to Direct Variation vs. Inverse Variation
then work the following word problems on your own sheet of notebook paper.
1. The number of chaperones, c, needed for the class trip varies directly as the number of students, s, going on the trip,
and c = 7 when s = 56. How many chaperones are needed if 104 students go on the class trip?
2. The number of pounds you weigh is directly proportional to the number of kilograms you are. Kay Dense steps onto
a scale calibrated in kilograms and finds that she is 50 kilograms. She knows that she weighs 110 pounds.
a. Write the particular equation expressing pounds in terms of kilograms.
b. How many pounds would a person weigh if the scale read
i. 100 kilograms?
ii. 25 kilograms?
iii. 150 kilograms?
c. How many kilograms would Stan Dupp be if he weighed 165 pounds?
d. How many kilograms are you?
e. What quantity does the constant of proportionality represent in the real world?
3. The time, 𝑡, that it takes for a group of volunteers to construct a house varies inversely as the number of volunteers,
𝑣. If 20 volunteers can build the house in 62.5 working hours, how many volunteers are needed to build a house in
50 working hours?
4. In Chemistry, you learn Boyle’s Law which states that the volume, v, of a fixed amount of gas (at constant
temperature) is inversely proportional to the pressure, p, of the gas.
a. Write the particular equation expressing volume in terms of pressure if a pressure of 46 pounds per
square inch (psi) compresses the gas to a volume of 360 cubic feet.
b. What pressure would be necessary to compress the gas to a volume of 276 cubic feet?
c. According to your equation, could you compress the gas to zero volume? Why or why not?