Question

John sells t-shirts. Plain shirts cost $5 and graphic shirts cost $7. In order to match his product costs, he must make at least $1,200.

a) Write an inequality to represent this situation.







b) If he sells 150 plain shirts and 60 graphic shirts, will he be able to cover
the product costs?







c)If he sells 90 graphic shirts, what’s the minimum number of plain shirts he must sell to break even?

Answer 1

a) 5x + 7y ≥ 1200

b) No.

c) A minimum of 114 plain t-shirts.

Explanation:

Given information:

• $5 = cost of one plain t-shirt.
• $7 = cost of one graphic t-shirt.
• $1200 = minimum revenue needed.

Define the variables:

• Let x = number of plain t-shirts.
• Let y = number of graphic t-shirts.

Part a

The inequality to represent the given information using the defined variables is:

• 5x + 7y ≥ 1200

Part b

Substitute x = 150 and y = 60 into the inequality:

⇒ 5(150) + 7(60) ≥ 1200

⇒ 750 + 420 ≥ 1200

⇒ 1170 ≥ 1200

As 1170 is not greater than or equal to 1200, John will not be able to cover the product costs if he sells 150 plain shirts and 60 graphic shirts.

Part c

Substitute y = 90 into the inequality and solve for x:

⇒ 5x + 7(90) ≥ 1200

⇒ 5x + 630 ≥ 1200

⇒ 5x + 630 - 630 ≥ 1200 - 630

⇒ 5x ≥ 570

⇒ 5x ÷ 5 ≥ 570 ÷ 5

⇒ x ≥ 114

Therefore, if John sells 90 graphic t-shirts, he must sell a minimum of 114 plain t-shirts to break even.