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?
This is the last question I need help with tonight, Thank you Jishka!
a. The profit when one shirt is purchased can be represented by the expression s - b, where s is the original selling price and b is the cost to the store to buy the shirts. The profit when two shirts are purchased can be represented by the expression 2s - (1/2)s - b, which simplifies to 3/2s - b.
To compare the profits, we want to set up an inequality that shows the store profits more from a customer purchasing two shirts than from a customer purchasing one shirt. In other words, we want to compare the expression s - b with the expression 3/2s - b. Since the store wants to make more profit by selling two shirts, the inequality would be:
3/2s - b > s - b
b. To isolate b in the inequality, we can start by subtracting s from both sides of the inequality:
3/2s - b - s > -b
Simplifying this expression:
1/2s - b > -b
Next, we can add b to both sides of the inequality:
1/2s > 0
This inequality states that the selling price (s) must be greater than zero in order for the store to make more profit by selling two shirts than selling one shirt. It means that the selling price should be positive.
c. If the store buys t-shirts for $12, we can substitute b = 12 into the inequality 1/2s > 0:
1/2s > 0
Substituting b = 12:
1/2s - 12 > 0
Next, we can isolate s by adding 12 to both sides:
1/2s > 12
Multiplying both sides by 2 to remove the fraction:
s > 24
Therefore, the selling price range that will make selling two shirts more profitable than selling one shirt is any selling price greater than $24.