Algebra Unit 8 Variation
Homework Day 2: Variation Word Problems
Name_________________________
Date____________________ Pd___
1. A theater company plans to hire people to build a stage set. The work time t (in hours per
person) varies inversely with the number of people hired p. The company estimates that 25
people working for 300 hours each can complete the job. Find the work time per person if
the company hires 30 people.
2. According to Charles’s Law, the volume of a gas and its temperature vary directly when
the pressure remains constant. If the volume of the gas at 291 K was 152 mL, what is the
volume of the gas at 305 K?
3. According to Boyle’s Law, the pressure and volume of a gas vary inversely if the
temperature is kept constant. If the gas has an initial volume of 2 L and a pressure of 3 atm,
find the pressure if the volume is decreased to 1.25 L.
4. A major snowstorm hit Virginia last week. In the first 2 hours of the storm, 5 inches of snow
fell. After 6 hours, 15 inches of snow had fallen. Does this represent a direct variation? Why
or why not?
5. Austin, Texas had a lot of rain yesterday. In the first 3 hours of the storm, 5 inches of rain
fell. After 5 hours, 10 inches had fallen. Does this represent a direct variation? Why or why
not?
6. The number s of tablespoons of sea salt needed in a saltwater fish tank varies
directly with the number w of gallons of water in the tank. A pet shop owner
recommends adding 100 tablespoons of sea salt to a 20 gallon tank.
a. Write a direct variation equation that relates w and s.
b. How many tablespoons of salt should be added to a 30 gallon saltwater fish tank?
7. Complete the chart with the correct property.
2(3𝑥 + 4) = 10
6𝑥 + 8 = 10
6𝑥 + 8 = 10
−8 − 8
6𝑥 + 0 = 2
6𝑥 = 2
1
1
(6𝑥) = (2)
6
6
𝑥=
1
3
Given