To find out how many hours Shantel must work to earn a monthly profit of at least $600, we can set up the following equation.
First, we need to determine her total revenue to achieve this profit level. Since she wants a profit of at least $600 and her expenses are $3,200, we can calculate the minimum revenue she needs:
\[ \text{Minimum Revenue} = \text{Expenses} + \text{Desired Profit} = 3,200 + 600 = 3,800 \]
Now, since she charges $25.00 per hour, we can denote the number of hours she works as \( h \). Thus, her total revenue can be expressed as:
\[ \text{Total Revenue} = 25h \]
To find the minimum hours she must work to earn at least $3,800, we can set up the inequality:
\[ 25h \geq 3,800 \]
Now we solve for \( h \):
\[ h \geq \frac{3,800}{25} \] \[ h \geq 152 \]
Therefore, to earn a monthly profit of at least $600, Shantel must work at least 152 hours each month.