To find out how many hours Shantel must work in order to earn a monthly profit of at least $600.00, we can set up the equation based on her earnings, expenses, and desired profit.
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Determine the profit requirement: Shantel wants to make at least $600.00 in profit each month, so her total income minus her expenses should be at least $600.00.
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Write the equation for profit: \[ \text{Total Income} - \text{Expenses} \geq \text{Desired Profit} \]
This translates to: \[ \text{Total Income} - 3200 \geq 600 \]
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Rearranging the equation: \[ \text{Total Income} \geq 3200 + 600 \] \[ \text{Total Income} \geq 3800 \]
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Express Total Income in terms of hours worked: Shantel charges $25.00 an hour. Therefore, if she works \(h\) hours, her total income will be: \[ \text{Total Income} = 25h \]
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Set up the inequality: \[ 25h \geq 3800 \]
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Solve for \(h\): Dividing both sides by 25: \[ h \geq \frac{3800}{25} \] \[ h \geq 152 \]
So, Shantel must work at least 152 hours each month to earn a monthly profit of at least $600.00.
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