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.
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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: \[ \text{Total Earnings} = 25h \]
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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: \[ \text{Profit} = 25h - 3200 \]
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Setting up the inequality for desired profit: We want her profit to be at least $600. Therefore, we set up the inequality: \[ 25h - 3200 \geq 600 \]
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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.
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