PSAT Math Multiple-Choice Question 610: Answer and Explanation

Question: 610

A salesperson earns a commission (C) on the number of phone plans sold (x) if the value of C is positive. (There is no penalty or cost to the salesperson for a negative value of C; simply no commission is paid.) The amount of commission in dollars is modeled by this equation:

C = 50x + 25(x - 100) - 2,000

What is the least number of phone plans that the salesperson must sell in order to earn a commission?

• A. 60
• B. 61
• C. 75
• D. 100

Correct Answer: B

Explanation:

(B) In order for the commission to be positive, change the expression to an inequality where the commission will be positive and solve for x:

C = 50x + 25(x - 100) - 2,000

0 < 50x + 25(x - 100) - 2,000

0 < 50x + 25x - 2,500 - 2,000

0 < 75x - 4,500

4,500 < 75x

60 < x

Since the salesperson cannot sell a partial phone plan, the least number of phone plans must be the first integer greater than 60, which is 61.