Question

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

The student council at Rockport High School is making T-shirts to sell for a fundraiser, at a price of $11 apiece. The costs, meanwhile, are $8 per shirt, plus a setup fee of $54. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?


Selling
shirts will cover the $
in costs.

Answer 1

Let \( x \) be the number of T-shirts sold.

The revenue from selling the T-shirts can be expressed as:
\[
\text{Revenue} = 11x
\]

The total costs consist of the variable cost per shirt and a fixed setup fee. Therefore, the total cost can be expressed as:
\[
\text{Cost} = 8x + 54
\]

To find the number of shirts needed to cover the costs, we set the revenue equal to the costs:
\[
11x = 8x + 54
\]

Now, we will solve the equation for \( x \):

1. Subtract \( 8x \) from both sides:
\[
11x - 8x = 54
\]
\[
3x = 54
\]

2. Divide both sides by 3:
\[
x = \frac{54}{3} = 18
\]

So, the student council must sell **18 shirts** to cover their costs.

Next, we will calculate the costs associated with selling 18 shirts:
\[
\text{Cost} = 8(18) + 54
\]
\[
= 144 + 54 = 198
\]

Thus, the costs will be **$198**.

To summarize the findings:
Selling **18** shirts will cover the **$198** in costs.