Algebra 2A
Variation Word Problems
Name _______________________________________
Direct, Joint and Inverse Variation
Directions: Write an appropriate variation equation, find the constant of variation, and solve for the
requested value.
1. y varies directly as x. y = 12 when x = 4, find y when x = 16.
2. y varies inversely as x. y = 2 when x = 16, find y when x = 20.
3. y varies directly as x squared. y = 800 when x = 10, find y when x = 3.
4. y varies inversely as x squared. y = 62.5 when x = 4, find y when x = 10.
5. y varies jointly as x and z. y = 10 when x = 25 and z = 2, find y when x = 4 and z = 3.
7. y varies jointly as x and z. y = 3 when x = 5 and z = 6, find y when x = 2 and z = 5.
8. The weight (w) of a shipment varies directly as the number (n) of books in the crate. When there are
10 books, the weight is 25 pounds. Find the weight when there are 30 books.
9. The amount of food (f) to prepare for a party varies directly as the number (n) of guests attending. If
there are to be 200 guests, the caterer will prepare 80 pounds of lasagna. How much lasagna should be
prepared if there are only 50 guests?
10. The amount of time (t) it takes to drive to Chicago varies inversely as the average (a) speed you
drive. If you drive 60 mph you can get there in 5 hours. How long will it take to get there if you drive
40 mph?
11. The power (p) in a resistance circuit varies jointly as the resistant (r) and the square of the current
(c). If a power of 50 watts results from a 10-ohm resistance with a 10 ampere current, find the resistance
when the power is 80 watts and the current is 2 amperes.
12. The length (l) that a spring will stretch varies directly as the amount (a) of weight on the end of the
spring. The spring stretches 18 inches with 2 pounds of weight on it. How long will it stretch with 5
pounds of weight on it?
13. The amount of time (t) it takes a painting crew to paint a house varies inversely as the number (n) of
painters on the crew. If it takes 3 hours for 6 people to paint the house, how long will it take 2 people to
paint the house?
14. The potential energy (e) of a stationary object varies jointly as the mass (m) and elevation (h) of the
object. If the potential energy is a 3-kg object whose elevation is 5m is 225 joules, then find the
elevation of an object if the potential energy is 120 joules and its mass is 2 kg.
15. The pressure (p) felt under water varies directly as the depth (d) of a diver. If the pressure is 20 ppsf
at 10 feet, what is the pressure at 50 feet?
16. An individual’s reaction time (t) varies inversely to the number of drinks (d) they have had. If after
2 drinks, the reaction time is 6 seconds, what is the reaction time after 6 drinks?
17. The area (a) of a circle varies directly as the square of the radius (r). If the radius is 10 cm, the area
is 314 square cm. What is the area if the radius is 15 cm?
18. The distance (d) an object falls is jointly proportional to the acceleration (a) due to gravity and the
square of time (t). If the acceleration due to gravity is 1 m/s2, the time is 2 seconds, and the distance it
falls is 174 m, how far does the object fall in 7 seconds?