You are starting a new business in which you have decided to sell two products, t-shirts and sweatshirts with your school logo. You have $500 available to start this business, meaning you cannot go over $500 when buying your products. The t-shirts will cost $2 each and the sweatshirts will cost $5 each. You plan on selling the t-shirts for $10 and the sweatshirts for $20. This is summarized in the chart below.

Question

You are starting a new business in which you have decided to sell two products, t-shirts and sweatshirts with your school logo. You have $500 available to start this business, meaning you cannot go over $500 when buying your products. The t-shirts will cost $2 each and the sweatshirts will cost $5 each. You plan on selling the t-shirts for $10 and the sweatshirts for $20. This is summarized in the chart below.
t-shirts
sweatshirts
Cost
$2
$5
Sell Price
$10
$20

a) Write an inequality for the total cost of your t-shirts and sweatshirts keeping in mind that the cost cannot exceed $500.

GPT 3.5 · Answer

Let x be the number of t-shirts and y be the number of sweatshirts.

The total cost of t-shirts is 2x and the total cost of sweatshirts is 5y.

Therefore, the inequality for the total cost of t-shirts and sweatshirts should not exceed $500:

2x + 5y ≤ 500