Suppose y varies directly with x, and y = 24 when x = 8. What is the value of y when x = 10?

First, you want to set up a proportion.

8/24 = 10/y

Cross multiply to get

240 = 8y, then divide 8 from both sides to get y = 30.

The statement suppose that y varies directly with x is best represented as:

y α x

To make it into equality, we insert a proportionality constant, k:

y = kx

Using the initial conditions, we solve for k.

y = kx

y = 24 when x = 8

24 = k (8)

k = 3

Thus, when x = 10,

y = 3 (10)

y = 30