Question

Suppose that f(x) varies directly with x and f(x) = 160 when x = 5.

What is f(x) when x = 0.5?

Answer 1

f(x) varies directly with x means: f(x) = kx where k is a constant.

when x = 5, f(x) = 160. Plug it into f(x) = kx.
160 = k(5). So k = 160/5 = 32

So f(x) = 32x

What is f(x) when x = 0.5
f(x) = 32(0.5) = 16.

Answer 2

A simpler way to do it is by proportion.
x = 0.5 is one tenth of x = 5.
Since this is a direct proportion problem, f(x) at x = 0.5 must also be one tenth of what f(x) is at x = 5 which is 1/10 * 160 = 16.