Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Ivan is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, he spent a total of $171. Ivan will be earning a base salary of $83 per month from the gym, plus an additional $8 for every class he teaches. If Ivan teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. How many classes will that take? How much will Ivan's expenses and earnings be?


Once Ivan teaches how many classes, his expenses and earnings will both be how much money
.

Answer 1

Let \( n \) be the number of classes Ivan teaches in his first month.

We can set up the earnings equation based on his base salary and the additional earnings from teaching classes:
\[
Earnings = 83 + 8n
\]

Ivan’s total expenses for certification were:
\[
Expenses = 171
\]

To find the number of classes he needs to teach to earn back his expenses, we set the earnings equal to the expenses:
\[
83 + 8n = 171
\]

Now, we can solve for \( n \):
1. Subtract 83 from both sides:
\[
8n = 171 - 83
\]
\[
8n = 88
\]

2. Divide both sides by 8:
\[
n = \frac{88}{8}
\]
\[
n = 11
\]

Now that we have found that Ivan needs to teach 11 classes, we can calculate his total earnings when he teaches that number of classes:
\[
Earnings = 83 + 8 \times 11
\]
\[
Earnings = 83 + 88
\]
\[
Earnings = 171
\]

Now we can fill in the blanks:

Once Ivan teaches **11** classes, his expenses and earnings will both be **$171**.