Question

challenge a customer at a clothing store is buying a pair of pants and a shirt. the store is having a 20%-off sale on all pants. the customer has a coupon for 10% off her entire purchase. the coupon cannot be combined with any other offers, so she can choose only one option. let n represent the original price of the pants and s represent the price of the shirt. write two equivalent expressions for each option. if the original cost of the pants is $15 and the shirt is $10, which option should the customer choose?

b. 0.8n + s
c. n + 0.8n − s
d. n − 0.20n + s
e. 0.20n + s

Explanation:

Step1: Analyze the discount on pants

The store has a 20% off sale on pants. So the customer pays 80% of the original price of pants. 80% as a decimal is 0.8, so the price of pants after discount is \(0.8n\) (where \(n\) is the original price of pants).

Step2: Add the price of the shirt

The price of the shirt is \(s\) (no discount mentioned for the shirt). So the total cost for the customer is the discounted price of pants plus the price of the shirt, which is \(0.8n + s\). Also, another equivalent expression: the discount on pants is 20% of \(n\), so the amount paid for pants is \(n-0.20n\), then adding the shirt price \(s\) gives \(n - 0.20n + s\).

Step3: Evaluate the options

• Option B: \(0.8n + s\) matches our first derived expression.
• Option D: \(n - 0.20n + s\) matches our second derived expression.
• Option A: Not relevant (no such form from our analysis).
• Option C: \(n + 0.8n - s\) is incorrect as we add the shirt price, not subtract.
• Option E: \(0.20n + s\) is incorrect as it would be a 80% increase on pants, not a discount.

Answer:

B. \(0.8n + s\), D. \(n - 0.20n + s\)