Question

Several students decide to start a T-shirt company. After initial expenses of $280, they purchase each T-shirt wholesale for $3.99. They sell each T-shirt for $10.99. How many must they sell to break even?

Answer 1

Answer:

They must sell 40 shirts to break even

Step-by-step explanation:

The break-even point is that point where the cost and revenue graphs intersect.

Up front,

expenditures are $280 + ($3.99)t, and this is to be set equal to revenue:  ($10.99)t:

$(\ 10.99)t = \ 280 + (\ 3.99)t.$

Begin solving this by subtracting ($3.99)t from both sides of this equation.  The result is

$(\ 10.99-\ 3.99t)t = \ 280 + (\ 3.99t - \ 3.99t)$

$\ 7t=\ 280t$

($7/shirt)t = $280.

Dividing both sides by ($7/shirt), we get

 $t=\frac{\ 280}{\ 7}$

t = $40

Revenue will equal costs (expenses) when these students have sold 40 shirts.

Therefore,they must sell 40 shirts to break even