PSAT Math Multiple-Choice Question 353: Answer and Explanation

Question: 353

Guests at a wedding had two meal choices, chicken and vegetarian. The catering company charges $12.75 for each chicken dish and $9.50 for each vegetarian dish. If 62 people attended the wedding and the catering bill was $725.25, which of the following systems of equations could be used to find the number of people who ordered chicken, c, and the number of people who ordered vegetarian, v, assuming everyone ordered a meal?

• A.
• B.
• C.
• D.

Correct Answer: C

Explanation:

C

Difficulty: Easy

Category: Word Problems

Getting to the Answer: Translate English into math. One equation should represent the total number of meals ordered, while the other equation should represent the cost of the meals.

The number of people who ordered chicken plus the number who ordered vegetarian equals the total number of people, 62, so one equation is c + v = 62. This means you can eliminate (A). Now, write the cost equation: the cost per chicken dish, $12.75, times the number of dishes, c, plus the cost per vegetarian dish, $9.50, times number of dishes, v, equals the total bill, $725.25. The cost equation should be 12.75c + 9.5v = 725.25. Together, these two equations form the system in (C).