PSAT Math Multiple-Choice Question 328: Answer and Explanation

Question: 328

A television set costs $25 less than twice the cost of a radio. If the television and radio together cost $200, how much more does the television cost than the radio?

• A. $50
• B. $75
• C. $100
• D. $125

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Substitution

Getting to the Answer: Translate English into math to write a system of equations with r as the cost of the radio in dollars and t as the cost of the television in dollars. A television costs $25 less than twice the cost of the radio, or t = 2r - 25. Together, a radio and a television cost $200, so r + t = 200.

The system of equations is:

The top equation is already solved for t, so substitute 2r - 25 into the second equation for t:

The radio costs $75, so the television costs 2(75) - 25 = 150 - 25 = $125. This means the television costs $125 - $75 = $50 more than the radio, which is (A).