Question

The student council at Silvergrove High School is making T-shirts to sell for a fundraiser, at a price of $10 apiece. The costs, meanwhile, are $7 per shirt, plus a setup fee of $45. Selling a certain number of shirts will allow the student council to cover their costs. What will the costs be? How many shirts must be sold?

Answer 1

EXPLANATION

Let's see the facts:

T-shirt sale price= $10

Cost = $7/shirt

Setup fee = $45

We have that selling a certain number of shirts will allow the students to cover their costs.

Cost= Setup fee + Unit Cost * Number of sold shirts

Let's call x to the number of sold shirts, the equation that represents the cost is:

Cost = 45 + 7x

Then, in order allow the students to cover their cost, the earns should be greater than the cost:

EARNS = COST

The equation that represents the earns is:

Earn= 10x

Now equaling the earns and the cost will give us the needed relationship:

10x = 45 + 7x

Subtracting 7x to both sides:

10x -7x = 45

Adding similar terms:

3x = 45

Dividing both sides by 3:

x = 45/3 = 15

So, 15 shirts should be sold to cover the costs.

The cost is:

Cost= 45 + 7*15 = 150

The cost is $150.