Question

Sharon runs a screen-printing business. To print T-shirts each day, it costs her $200 in labor plus $5 per T-shirt for materials. Her income is $15 for each T-shirt she sells. How many T-shirts does Sharon need to sell each day in order for her costs to equal her income for that day?

(i mainly need the equation for this problem)

Answer 1

Equation: 15n = 200 + 5n

Number of T-shirts: 20

Explanation:

We need to find an expression for the costs for 1 day for making n number of T-shirts and an expression for the income for 1 day for selling n number of T-shirts. Then we set the expressions equal and solve for n, the number of T-shirts.

Expenses in 1 day:

The expenses are a fixed cost of $200 plus the cost per T-shirt.

$200 plus $5 per T-shirt

We need an expression for the cost per T-shirt in terms of n, the number of T-shirts.

If she makes 1 T-shirt, she spends $5 * 1.

If she makes 2 T-shirts, she spends $5 * 2.

If she makes n T-shirts, she spends $5 * n, or simply 5n.

Her total costs for a day are:

200 + 5n

Income in 1 day:

All the income comes from selling T-shirts.

She sells 1 T-shirt for $15 * 1.

She sells 2 T-shirts for $15 * 2.

She sells n T-shirts for $15 * n, or simply 15n

Her total income for 1 day is:

15n

Now we set the costs equal to the income and solve for n.

15n = 200 + 5n <--------- here is the equation you need

Subtract 5n from both sides.

10n = 200

Divide both sides by 10.

n = 20

Answer: She needs to sell 20 T-shirts.