Logan made a profit of $350 as a mobile groomer. He charged $55 per appointment and received $35 in tips, but also had to pay a rental fee for the truck of $10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had

1 answer

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 \( x \):

  1. Subtract 35 from both sides:

\[ 45x = 350 - 35 \] \[ 45x = 315 \]

  1. Divide both sides by 45:

\[ x = \frac{315}{45} \] \[ x = 7 \]

Therefore, Logan had 7 appointments.