Jill is a writing tutor at her local community center. She has spent $400 on advertisements, and she pays the community center $20 per hour to use its facilities. She charges her clients $60 per hour.

Question

How many hours must Jill tutor for the amount she brings in to equal the amount she spends?

Answer 1

To find out how many hours Jill must tutor for her revenue to equal her expenses, we can set up an equation based on her costs and income.

Let \( h \) be the number of hours that Jill tutors.

Expenses:

1. Advertising costs: $400
2. Facility rental costs: $20 per hour, so for \( h \) hours, the cost is \( 20h \).

Total expenses can be calculated as: \[ \text{Total Expenses} = 400 + 20h \]

Revenue: Jill earns $60 per hour for tutoring, so for \( h \) hours, her income is: \[ \text{Total Revenue} = 60h \]

To find the break-even point (where income equals expenses), we set the total revenue equal to the total expenses: \[ 60h = 400 + 20h \]

Now, we can solve for \( h \):

1. Subtract \( 20h \) from both sides: \[ 60h - 20h = 400 \] \[ 40h = 400 \]

2. Divide both sides by 40: \[ h = \frac{400}{40} = 10 \]

Jill must tutor for 10 hours in order to cover all of her expenses.