Question

The student council at Newberg High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $7 per shirt, plus a setup fee of $65. 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?

Answer 1

The student council's costs will be $146 and they need to sell 13 shirts to cover their costs.

Explanation:

Let's call the number of shirts sold "x".

The revenue from selling x shirts at $12 each is:

• Revenue = 12x

The total cost of making x shirts is:

• Total Cost = 7x + 65

In order to break even (i.e. cover their costs), the revenue must equal the total cost:

`\sf:\implies 12x = 7x + 65`

Solving for x:

`\sf:\implies 5x = 65`

`\sf:\implies \boxed{\bold{\:\:x = 13\:\:}}\:\:\:\green{\checkmark}`

Therefore, the student council must sell 13 shirts to break even.

To find the total costs, we can substitute x = 13 into the total cost equation:

`\sf:\implies Total\: Cost = 7(13) + 65 = \boxed{\bold{\:\:\$146\:\:}}\:\:\:\green{\checkmark}`

So the student council's costs will be $146 and they need to sell 13 shirts to cover their costs.

Answer 2

Let's assume that the number of shirts that must be sold to cover the costs is x.

The revenue from selling x shirts is 12x dollars, and the total cost is the sum of the setup fee and the cost per shirt multiplied by the number of shirts, which is 65 + 7x dollars.

To break even, the revenue must be equal to the cost:

12x = 65 + 7x

Subtracting 7x from both sides:

5x = 65

Dividing both sides by 5:

x = 13

Therefore, the student council must sell 13 shirts to break even.

To find the total costs, we can substitute x = 13 into the expression for the total cost:

65 + 7x = 65 + 7(13) = 156

So the total costs will be $156.