Joint and Combined Variation Answers

The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?

A quantity m varies jointly with p and r. When p is 2 and r is 4, m is 1. What is the constant of variation?

The amount of time it takes p people to paint d doors varies directly with the number of doors and inversely with the number of people. Four people can paint 10 doors in 2 hours. How many people will it take to paint 25 doors in 5 hours?

A quantity b varies jointly with c and d and inversely with f. When c is 4, d is 9, and f is 6, b is 18. What is the constant of variation?

A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation, k?

The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant of variation?

It takes 4 lawnmowers to cut 2 acres of grass in 2 hours. If the amount of time varies directly with the amount of grass and inversely with the number of lawnmowers, how many hours will it take 2 lawnmowers to cut 6 acres of grass?

When f = 2 and g = 8, n = 4. If n varies jointly with f and g, what is the constant of variation?

A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?

The quantity a varies directly with b and c and inversely with d. The quantity d is tripled. Which of the following could be true if the relationship remains the same?

The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant. The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters. A second rectangular prism with the same height as the first prism has a length of 12 centimeters and a width of 8 centimeters. What is the volume of the second prism?

When y is 4, p is 0.5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?

When h is and j is , g is 4. If g varies jointly with h and j, what is the value of g when h is 2 and j is 3?