Answer:
Equation: [tex]P = 10n[/tex]
[tex]P = 40[/tex] 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
[tex]P = kn[/tex]
When P = 150, n = 15 (Substitute these values in the given equation)
[tex]150 = k * 15[/tex]
Divide both sides by 15
[tex]\frac{150}{15} = \frac{k * 15}{15}[/tex]
[tex]10 = k\\k = 10[/tex]
Substitute k = 10 in [tex]P = kn[/tex]
[tex]P = 10 * n[/tex]
[tex]P = 10n[/tex] ------- Equation that relates P and n
When she sold 4 necklaces, n = 4
Substitute n = 4 in the formula above
[tex]P = 10 * 4[/tex]
[tex]P = 40[/tex]
