To determine how many hours Shantel must work each month to earn a monthly profit of at least $600, we can follow these steps:
- Define Total Income: Shantel charges $25.00 per hour per student. Let \( H \) be the number of hours she works. Therefore, her total income from one student is:
\[ \text{Total Income} = 25 \times H \]
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Define Total Expenses: Her monthly expenses are given as $3,200.00.
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Define Profit: Profit is defined as total income minus total expenses. Thus, the profit can be expressed as:
\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} \]
Substituting the known values:
\[ \text{Profit} = (25 \times H) - 3200 \]
- Set Profit Condition: She wants the profit to be at least $600. Thus, we set up the inequality:
\[ (25 \times H) - 3200 \geq 600 \]
- Solve for \( H \):
- Adding $3,200 to both sides:
\[ 25 \times H \geq 600 + 3200 \]
\[ 25 \times H \geq 3800 \]
- Dividing both sides by 25:
\[ H \geq \frac{3800}{25} \]
\[ H \geq 152 \]
Therefore, Shantel must work at least 152 hours each month to earn a monthly profit of at least $600.00.