Joint and Combined Variation Answers

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

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?

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?

The kinetic energy, K, of an object varies jointly with the mass of the object and the square of the velocity of the object. A 50-kg object moving at a velocity of 20 meters per second has 10,000 joules of kinetic energy. How many joules of kinetic energy does a 25-kg object moving at a velocity of 10 meters per second have?

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?

When a = 6 and b = 22, c = 33. If c varies directly with b and inversely with a, which equation models the situation?

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?

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 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?