Joint Variation Practice
Math 2
Name __________________________
Find the value of the variable for each question.
1. y varies jointly as x and z. If y = 5 when x = 3, and z = 4, find y when x= 6 and z = 8.
2. y varies jointly as x and z. If y = 12 when x = 4, and z = 3, find y when x= 9 and z = 8.
3. A varies jointly as b and h. If A = 16 when b = 2, and h = 8, find A when b= 8 and h = 16.
4. y varies jointly as x and √ . If y = 6 when x = 3, and z = 9, find y when x= 4 and z = 36.
5. y varies jointly as √ and z2. If y = 3 when x = 8 and z = 4, find y when x = 27 and z = 6.
6. x varies jointly as y3 and √ . If x = 7 when y = 2 and z = 4, find x when y = 3 and z = 9.
In exercises 7 – 9, the variable z varies jointly with the product of x and y. Use the given values
to find an equation that relates the variables.
7. x = 3, y = 8, and z = 2
8. x = -5, y = 2, z = ¾
9. x = 1, y = ½ , z = 4
10. Strawberries varied jointly as plums and tomatoes. If 500 strawberries went with 4 plums and 25
tomatoes, how many plums would go with 40 strawberries and 2 tomatoes?
Joint Variation Practice
Math 2
Name __________________________
11. The cost, c, of materials for a deck varies jointly with the width, w, and the length, l. If c = $470.40
when w =12 and l = 16, find the cost when w = 10 and l = 25.
12. The value of real estate V varies jointly with the neighborhood index N and the square footage of
the house S. If V = $376, 320 when N = 96 and S = 1600, find the value of a property with N = 83 and
S = 2150.
13. The number of gallons, g, in a circular swimming pool varies jointly with the square of the radius r2
and the depth d. If g = 754 when r = 4 and d = 2, find the number of gallons in the pool when r = 3 and
d = 1.5
14. Cheers varied jointly as the number of fans and the square of the jubilation factor. When there
were 100 fans and jubilation factor was 4 there were 1000 cheers. How many cheers were there when
there were only 10 fans whose jubilation factor was 20?
15. The work accomplished varied jointly as the number of people and their average productivity factor.
If 100 people with an average productivity factor of 20 could produce 8000 units on one shift, how many
people whose factor was only 2 would be required to produce 16,000 units?
16. The number of students varied jointly as the number of teachers and the number of administrators
squared. 1000 students were present when there were 5 teachers and 2 administrators. How many
students were there with 8 teachers and 1 administrator?