Question

irene starts with $50 in her bank account, and she earns $12 per hour babysitting. malik starts with $14 in his bank account, and he earns $15 per hour mowing lawns. they both put the money they earn directly into their accounts. the variable t represents the number of hours they worked. after how many hours of work will irene and malik have the same total amount of money in their accounts? how much money will they have at that time? how much money will they each have at that time? you can substitute 12 for t in irene’s or malik’s expression to help you solve. solve on paper, then enter your answer on zearn.
irene’s total dollars after t hours: 50 + 12t
malik’s total dollars after t hours: 14 + 15t
irene’s total: 50 + 12t
malik’s total: 14 + 15t
t = 12
irene and malik will each have $\square$ after working 12 hours.

Explanation:

Step1: Calculate Irene's total after 12h

Substitute $t=12$ into $50+12t$:

$$\begin{align*} 50 + 12\times12 &= 50 + 144\\ &= 194 \end{align*}$$

Step2: Calculate Malik's total after 12h

Substitute $t=12$ into $14+15t$:

$$\begin{align*} 14 + 15\times12 &= 14 + 180\\ &= 194 \end{align*}$$

Step3: Find time when totals are equal

Set expressions equal, solve for $t$:
$50 + 12t = 14 + 15t$
Subtract $12t$ from both sides:
$50 = 14 + 3t$
Subtract 14 from both sides:
$36 = 3t$
Divide by 3:
$t = 12$

Step4: Verify equal total at $t=12$

Use either expression, e.g., $50+12\times12=194$

Answer:

1. Irene and Malik will each have $\$194$ after working 12 hours.
2. After 12 hours of work, Irene and Malik will have the same total amount of money, which is $\$194$.