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.
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!
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
a. The profit when one shirt is purchased is given by s - b, where s represents the selling price and b represents the cost to the store to buy the shirts. To find the profit when two shirts are purchased, we can denote the half-price of the second shirt as 0.5(s - b), since the second shirt is sold at half the price. Therefore, the profit when two shirts are purchased is given by s - b + 0.5(s - b).
To compare the profits, we can write the inequality:
s - b + 0.5(s - b) > s - b
b. To isolate b in the inequality, we can simplify it:
s - b + 0.5s - 0.5b > s - b
Combining like terms:
1.5s - 1.5b > s - b
Removing parentheses:
1.5s - 1.5b > s - b
Combining like terms:
0.5s > 0.5b
Dividing both sides by 0.5:
s > b
The inequality s > b implies that the selling price should be greater than the cost to the store for it to be more profitable to sell two shirts instead of one. This makes sense because the store needs to ensure that they make more money in revenue (selling price) than they spend on buying the shirts (cost).
c. Given that the store buys t-shirts for $12 (b = 12), we can substitute this value into the inequality s > b and solve for the selling price range.
s > 12
This means that the selling price (s) must be greater than $12 for selling two shirts to be more profitable than selling one shirt. The selling price can range anywhere from slightly above $12 to infinitely higher, as long as it is greater than $12.