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? write an expression to represent the amount of money irene has after t hours, where t represents the number of hours worked.

Explanation:

Step1: Define Irene's total money

Irene starts with $50, earns $12 per hour.
Expression: $50 + 12t$

Step2: Define Malik's total money

Malik starts with $14, earns $15 per hour.
Expression: $14 + 15t$

Step3: Set equal for same total

Set the two expressions equal to find $t$.
$50 + 12t = 14 + 15t$

Step4: Solve for $t$

Subtract $12t$ and 14 from both sides.
$50 - 14 = 15t - 12t$
$36 = 3t$
$\frac{36}{3} = t$
$t = 12$

Step5: Calculate total money at $t=12$

Substitute $t=12$ into Irene's expression.
$50 + 12(12) = 50 + 144 = 194$

Answer:

1. Expression for Irene's money: $\boldsymbol{50 + 12t}$
2. They will have the same amount after $\boldsymbol{12}$ hours.
3. At that time, they each have $\boldsymbol{\$194}$.