PSAT Math Multiple-Choice Question 335: Answer and Explanation

Question: 335

At a certain restaurant, there are 25 tables and each table has either 2 or 4 chairs. If a total of 86 chairs accompany the 25 tables, how many tables have exactly 4 chairs?

• A. 7
• B. 12
• C. 15
• D. 18

Correct Answer: D

Explanation:

D

Difficulty: Hard

Getting to the Answer: Create a system of two linear equations where t represents tables with 2 chairs and f represents tables with 4 chairs. The first equation should represent the total number of tables, each with 2 or 4 chairs, or t + f = 25. The second equation should represent the total number of chairs. Because t represents tables with 2 chairs and f represents tables with 4 chairs, the second equation should be 2t + 4f = 86. Now, solve the system using substitution. Solve the first equation for t in terms of f so that when you substitute the result into the second equation, you can solve directly for f:

There are 18 tables with 4 chairs each, (D). This is all the question asks for, so you don't need to find the value of t.