Question

Pam recently started selling custom T-shirts online. She spent $504 on screen-printing tools, and she spends $4.50 per shirt on supplies. She is selling each shirt for $15.
Which equation can you use to find s, the number of T-shirts Pam must sell for her sales to equal her expenses?
How many T-shirts must Pam sell for her sales to equal her expenses?
T-shirts

Answer 1

To determine the number of T-shirts Pam must sell for her sales to equal her expenses, we can set up an equation based on her costs and revenues.

### Expenses:
Pam has fixed costs from the screen-printing tools and variable costs per shirt:
- Fixed costs (tools) = $504
- Variable cost per shirt = $4.50

So, her total expense for selling \( s \) shirts can be expressed as:
\[
\text{Total Expenses} = 504 + 4.50s
\]

### Revenue:
Pam's revenue from selling \( s \) shirts at $15 each is:
\[
\text{Total Revenue} = 15s
\]

### Setting the equation:
To find the number of shirts \( s \) that Pam must sell for her sales to equal her expenses, we set up the equation:
\[
15s = 504 + 4.50s
\]

### Solving the equation:
1. Subtract \( 4.50s \) from both sides:
\[
15s - 4.50s = 504
\]
\[
10.50s = 504
\]

2. Divide both sides by \( 10.50 \):
\[
s = \frac{504}{10.50}
\]
\[
s = 48
\]

### Conclusion:
Pam must sell **48 T-shirts** for her sales to equal her expenses.