Question

Theodore and Sarah have a small business selling custom-made T-shirts. They currently sell 175 shirts per month and charge $15 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 the number of T-shirts they sell
by 8 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
R(x) =
Keypad
Keyboard Shortcut

Answer 1

The total monthly revenue that Theodore and Sarah's business can generate can be represented by the equation:

R(x) = (175 - 8x)(15 + x)

Why? This is because for each $1 increase in price, the number of T-shirts sold decreases by 8, so the total number of T-shirts sold would be 175 - 8x. The selling price per T-shirt would be $15 + $x. Multiplying these two quantities gives the monthly revenue. Simplifying this expression gives:

R(x) = 2625 + 7x - 8x^2

Therefore, the expression for the total monthly revenue that Theodore and Sarah's business can generate if they change the selling price of their T-shirts is R(x) = 2625 + 7x - 8x^2.