To create an equation that represents Logan's situation, we can define the number of appointments he made as \( x \).
Income from appointments:
- Logan charges $55 per appointment.
- Total income from appointments is \( 55x \).
Income from tips:
- Total income from tips is $35.
Total income:
- Total income = Income from appointments + Income from tips
- \( \text{Total income} = 55x + 35 \)
Expenses:
- Logan pays a rental fee of $10 per appointment.
- Total expenses from the rental fee is \( 10x \).
Profit:
- Profit is defined as total income minus total expenses.
- According to the problem, his profit is $350.
So, we can set up the equation as follows:
\[ \text{Total income} - \text{Total expenses} = \text{Profit} \]
Substituting the expressions we found:
\[ (55x + 35) - (10x) = 350 \]
Now simplify the equation:
\[ 55x + 35 - 10x = 350 \] \[ 45x + 35 = 350 \]
Next, isolate \( x \):
- Subtract 35 from both sides:
\[ 45x = 350 - 35 \] \[ 45x = 315 \]
- Divide both sides by 45:
\[ x = \frac{315}{45} \] \[ x = 7 \]
Therefore, Logan had 7 appointments.