PSAT Math Multiple-Choice Question 351: Answer and Explanation

Question: 351

At a certain coffee store, the small bag of beans costs $2.50 and the large bag of beans costs $15. If the store sold 27 small and large bags of beans and had $155 in revenue in one week, how many small bags and large bags of beans were sold?

• A. 20 small bags, 7 large bags
• B. 7 small bags, 20 large bags
• C. 8 small bags, 19 large bags
• D. 20 small bags, 9 large bags

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Combination

Getting to the Answer: Choose intuitive letters for the variables: s for the small bags, L for the large bags. You're given the cost of each, as well as the number of each sold and the total revenue generated. Next, write the system of equations that represents the information given:

Multiplying the top equation by -15 allows you to solve for s using combination:

Solving for s gives 20, which eliminates (B) and (C). Plugging this value back into the first equation allows you to find L, which is 7. Choice (A) is correct.