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

Question

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.