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

Answer:

Equation: $P = 10n$

$P = 40$ when n = 4

Step-by-step 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

$\frac{150}{15} = \frac{k * 15}{15}$

$10 = k\\k = 10$

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

$P = 10 * 4$

$P = 40$