Question

The amount of money Sally earns, P, varies directly with the number, n, of necklaces she sells. When Sally sells 15 necklaces, she earns $150. Write the equation that relates P and n. How much money would she earn if she sold 4 necklaces?

Answer 1

Equation:
`P = 10n`

`P = 40` when n = 4

Explanation:

Given

Direct Variation: P ∝ n

When n = 15, P = 150

Required

Determine the equation

Her earnings if she sold 4 necklaces

P ∝ n

Convert variation to equation

`P = kn`

When P = 150, n = 15 (Substitute these values in the given equation)

`150 = k * 15`

Divide both sides by 15

`(150)/(15) = (k * 15)/(15)`

`10 = k\\k = 10`

Substitute k = 10 in
`P = kn`

`P = 10 * n`

`P = 10n` ------- Equation that relates P and n

When she sold 4 necklaces, n = 4

Substitute n = 4 in the formula above

`P = 10 * 4`

`P = 40`