A clothing store is holding a ‘buy one, get one half off’ sale for t-shirts, where the second t-shirt purchased is half the original price.

Question

a. Let b be the cost to the store to buy the shirts, and let s be the
original selling price. Write an inequality relating the two
variables such that the store profits more from a customer
purchasing two t-shirts than from a customer purchasing one.
(Hint: The expression s – b represents the profit when one shirt
is purchased. What is an expression for the profit when two
shirts are purchased?)
b. Isolate b in the inequality. Explain what the inequality says about the buying and selling prices.
c. If the store buys t-shirts for $12, what selling price range will make selling two t-shirts more profitable than selling one t-shirt?
Thank you Jishka!

Answer 1

since the 2nd shirt sells for half price, its profit is s/2 - b
so you want
(s-b) + (s/2 - b) > (s-b)
s/2 - b > 0
s > 2b

now finish it off