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?
hours

Answer 1

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

Jill's costs include her advertisement expenses and the facility fee for tutoring. Her total expenses can be expressed as:

\[ \text{Total Costs} = \text{Advertisement Costs} + \text{Facility Costs} \] \[ \text{Total Costs} = 400 + 20h \]

Jill's income from tutoring can be expressed as:

\[ \text{Total Income} = \text{Charge per Hour} \times \text{Number of Hours} \] \[ \text{Total Income} = 60h \]

To find the number of hours \( h \) she must tutor so that her income equals her expenses, we set her total income equal to her total costs:

\[ 60h = 400 + 20h \]

Now, we can solve for \( h \). First, we'll subtract \( 20h \) from both sides:

\[ 60h - 20h = 400 \] \[ 40h = 400 \]

Next, we divide both sides by 40:

\[ h = \frac{400}{40} = 10 \]

Thus, Jill must tutor for 10 hours for the amount she brings in to equal the amount she spends.