Question

The amount of money Sally earns in dollars, P, varies directly with the number, n, of necklaces she sells. When Sally sells 15 necklaces she earns $150.

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`