Question

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

Answer 1

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.

Answer 2

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