Question

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

Answer 1

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:

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

2. Divide both sides by 45:

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

Therefore, Logan had **7 appointments**.