Joint Variation Word Problems

The variable x is in joint variation with y and z. When the values of y and z are 4 and 6, x is 16. What is the value of x when y = 8 and z =12?

• 32

• 64

• 48

• 96

A is in joint variation with B and square of C. When A = 144, B = 4 and C = 3. Then what is the value of A when B = 6 and C = 4?

• 12

• 24

• 36

• 48

If y varies jointly with the product of x and z, and y = 105 when x = 5 and z = 7, find y when x = 9 and z = 10.

• 270

• 180

• 360

• 255

If y varies jointly with the product of x and z, and y = 1000 when x = 10 and z = 20, find y when x = 8 and z = 10.

• 100

• 200

• 300

• 400

The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the cube of the diameter. If the shaft of a certain material 3 inches in diameter can transmit 45 hp at 100 rpm, what must the diameter be in order to transmit 60 hp at 150 rpm?

• 24

• 12

• 24

• 36

• 48

Suppose y varies jointly as x & z. 
If y = -180 when z = 15
and x = -3,
then find y when x = 7 and z = -5.

• -140

• 140

• -4

• 4

The equation    
w = 10chs  represents:

• direct variation

• inverse variation

• joint variation

• none of these

The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the

velocity. If a wind blowing at 50 mph exerts a force of 75 pounds on a surface of 500 ft², how much force will a

wind of 75 mph place on a surface of 10 ft²?

• 2.25 pounds

• 3.375 pounds

• 0.67 pounds

• 1 pound