Question

Shantel offers online tutorial services. She charges $25.00 an hour per student. Her budget tracker reflects a total of $3,200.00 monthly expenses. How many hours must she work each month to earn a monthly profit of at least $600.00?

Answer 1

To determine how many hours Shantel must work to earn a monthly profit of at least $600.00, we can set up the following equations based on her earnings, expenses, and desired profit.

1. **Total earnings from tutoring**:
\[
\text{Total Earnings} = \text{Hourly Rate} \times \text{Hours Worked}
\]
Given her hourly rate is $25.00, if \( h \) is the number of hours she works, her total earnings can be expressed as:
\[
\text{Total Earnings} = 25h
\]

2. **Profit calculation**:
Profit is calculated by subtracting her monthly expenses from her total earnings:
\[
\text{Profit} = \text{Total Earnings} - \text{Expenses}
\]
Here, her expenses are $3,200. Thus, the profit equation becomes:
\[
\text{Profit} = 25h - 3200
\]

3. **Setting up the inequality for desired profit**:
We want her profit to be at least $600. Therefore, we set up the inequality:
\[
25h - 3200 \geq 600
\]

4. **Solving the inequality**:
Start by isolating \( 25h \):
\[
25h \geq 600 + 3200
\]
\[
25h \geq 3800
\]
Now, divide both sides by 25 to solve for \( h \):
\[
h \geq \frac{3800}{25}
\]
\[
h \geq 152
\]

Thus, Shantel must work at least **152 hours** per month to earn a monthly profit of at least $600.00.