Question

problems 3–4
prisha and mia agree to go to the movies after they have earned the same amount of money for the same number of hours worked.

• mia earns $7 per hour mowing her neighbors’ lawns. she also earned $14 one time for hauling away bags of recyclables.
• prisha babysits her neighbor’s children. the table shows the amount of money, m, she earns in h hours.

h	m
2	$16.80
3	$25.20

how many hours do they each have to work before they go to the movies?
how much will each of them have earned?

Explanation:

Part 1: Hours to Work

Step1: Define Earnings Equations

Mia's earnings: \( M = 7h + 14 \) (7 per hour + 14 one - time).
Prisha's earnings: From the table, rate is \( \frac{8.40}{1}=8.4 \) per hour, so \( P = 8.4h \).

Step2: Set Equations Equal

To find when earnings are equal: \( 7h + 14 = 8.4h \).

Step3: Solve for \( h \)

Subtract \( 7h \) from both sides: \( 14 = 1.4h \).
Divide both sides by 1.4: \( h=\frac{14}{1.4}=10 \).

Step1: Use Prisha's Earnings Formula

Prisha's formula: \( P = 8.4h \). We know \( h = 10 \), so \( P = 8.4\times10 \).

Step2: Calculate Earnings

\( 8.4\times10 = 84 \). (We could also use Mia's formula: \( 7\times10 + 14=70 + 14 = 84 \))

Answer:

10

Part 2: Earnings Amount