PSAT Math Multiple-Choice Question 347: Answer and Explanation

Question: 347

A bed costs $40 less than three times the cost of a couch. If the bed and couch together cost $700, how much more does the bed cost than the couch?

• A. $185
• B. $225
• C. $330
• D. $515

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Substitution

Getting to the Answer: Write a system of equations where c is the cost of the couch in dollars and b is the cost of the bed in dollars. A bed costs $40 less than three times the cost of the couch, or b = 3c - 40. Together, a bed and a couch cost $700, so b + c = 700.

The system of equations is:

The top equation is already solved for b, so substitute 3c - 40 into the bottom equation for b and solve for c:

Remember to check if you solved for the right thing! The couch costs $185, so the bed costs 3($185) - $40 = $555 - $40 = $515. This means the bed costs $515 - $185 = $330 more than the couch. Therefore, (C) is correct.