Question

A high school purchases a printing machine that can put lettering on clothing for $6,000. The school plans to print T-shirts with the school logo and sell them. Each T-shirt costs the school $4 and will sell for $12. How many T-shirts must the school sell before breaking even?

Answer 1

The answer is 175 so u just divide

Answer 2

Let's assume

number of T-shirts is x

Firstly , we will find cost function

Calculation of cost function:

A high school purchases a printing machine that can put lettering on clothing for $6,000

so, cost of printing machine =$6000

initial cost =6000

Each T-shirt costs the school $4

so, total cost =6000+4*x

`C(x)=6000+4x`

Calculation of selling price function:

we are given

Each T-shirt costs the school will sell for $12

so,

total selling price =12x

`S(x)=12x`

Break-even point:

In break-even point , selling price = cost price

so,

`S(x)=C(x)`

now, we can plug value

`12x=6000+4x`

now, we can solve for x

`12x-4x=6000`

`8x=6000`

`x=750`

So, the number of T-shirts are 750.........Answer