Question

Theodore and Sarah have a small business selling custom-made T-shirts. They currently sell 250 shirts per month and charge $12 per T-shirt. Sarah thinks they can increase their revenue by increasing their selling price, but Theodore knows from experience that each $1 increase in price will decrease thenumber of T-shirts they sell by 7 shirts per month. Find an expression for the total monthly revenue Theodore and Sarah's business can generate if they change the selling price of their T-shirts. Let x represent the number of $1 increases in the price of the T-shirts.

Answer 1

we are told that x should represent the number of $1 increases in price of the tshirts.

each $1 increase = decrease in the number of shirts sold by 7

if the price increases once, that is a $1 increase and the number of shirts decreases by 7

if it increases by 2, that is a $2 increase and the number of shirts would decrease by 2 times 7 = 14

if it decreases x times, the number of shirts would decrease by 7x

Therefore, the expression for the revenue would be

(12 + x)(250 - 7x)