Jill teaches a music class for toddlers at the mall. This month, she spent $525 on instruments, and the mall charged her $40 per class to use its facilities. She is paid $65 for each class she teaches.

Question

How many classes must Jill teach this month for the amount she brings in to equal her expenses?
classes

Answer 1

To find out how many classes Jill must teach for her income to match her expenses, we can set up the equation based on her total expenses and income per class.

1. Calculate total expenses:

   • Instruments cost: $525
   • Facility charge per class: $40
   • Instructor payment per class: $65

   Therefore, the total expense per class is: \[ \text{Total Expense per Class} = \text{Facility Charge} + \text{Instructor Payment} \] \[ \text{Total Expense per Class} = 40 + 65 = 105 \]

   Thus, if she teaches \( x \) classes, her total expenses for \( x \) classes will be: \[ \text{Total Expenses} = 525 + 105x \]

2. Calculate total income:

   • She earns $65 per class, so for \( x \) classes: \[ \text{Total Income} = 65x \]

3. Set the total income equal to total expenses: \[ 65x = 525 + 105x \]

4. Rearranging the equation: \[ 65x - 105x = 525 \] \[ -40x = 525 \] \[ x = \frac{525}{40} \] \[ x = 13.125 \]

Since Jill cannot teach a fraction of a class, she needs to round up. Therefore, Jill needs to teach 14 classes to ensure her income exceeds her expenses.

Thus, the final answer is: \[ \boxed{14} \]