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.
b) Graph the inequality from part a). You can let the x-axis represent the number of t-shirts you make and the y-axis represent the number of sweatshirts you make. Limit your graph to just positive x and y values (i.e. there is no need to shade anything in the

GPT 3.5 · Answer

a) Let x be the number of t-shirts and y be the number of sweatshirts. The total cost equation is:

$2x + $5y ≤ $500

b) To graph the inequality $2x + $5y ≤ $500, we can plot the points (0, 100), (0, 0), (250, 0), and (0, 100) and draw a line through these points. The line should go through the first and third quadrant, because negative values of x and y do not make sense in this context.