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.

Question

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.