PSAT Math Multiple-Choice Question 329: Answer and Explanation

Question: 329

At a snack stand, hot dogs cost $3.50 and hamburgers cost $5.00. If the snack stand sold 27 snacks and made $118.50 in revenue, how many hot dogs and how many hamburgers were sold?

• A. 16 hot dogs; 11 hamburgers
• B. 16 hot dogs; 16 hamburgers
• C. 11 hot dogs; 14 hamburgers
• D. 11 hot dogs; 16 hamburgers

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Combination

Getting to the Answer: Begin by translating English into math. Define the variables logically: d for hot dogs, b for hamburgers. You're given the cost of each, as well as the number of snacks sold and the total revenue generated. Next, write the system of equations that represents the information given:

Multiplying the top equation by -5 allows you to solve for d using combination:

Dividing both sides by -1.5 gives d = 11, which eliminates (A) and (B). Plugging 11 in for d in the first equation in the system gives you 11 + b = 27. Subtract 11 from both sides to find that b = 16.(D) is correct.