PSAT Math Multiple-Choice Question 128: Answer and Explanation

Question: 128

Stephen takes out an interest-free loan from his friend. Each month he makes a payment to his friend. The amount of money that Stephen still owes his friend is given by the equation y = 1,200 - 75m, in which m is the number of months since the loan was made and y is the money, in dollars, that Stephen still owes. Which of the following best describes the meanings of the constant and coefficient in this equation?

• A. The number 75 is the rate of decrease, in dollars per month, in the amount Stephen owes his friend, which started at $1,200.
• B. The number 75 is the number of months it will take Stephen to pay off the loan, which was for $1,200.
• C. The number 75 is the rate of increase, in dollars per month, that Stephen owes his friend for the loan, which started at $1,200.
• D. The number 75 is the rate of increase, in dollars per month, of Stephens payments on the loan, which was for $1,200.

Correct Answer: A

Explanation:

A

The question asks for the meaning of the constant and coefficient in the equation. Label the parts of the equation with the information given. The question states that m is the number of months since the loan was made, and y is the money, in dollars, that Stephen still owes. Therefore, the equation is the money, in dollars, that Stephen still owes = 1,200 - 75(the number of months since the loan was made). Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) states that 75 is the rate of decrease in dollars per month and $1,200 is the original amount of the loan. Since 75 is multiplied by the number of months since the loan was made, and that term is subtracted from 1,200, this is consistent with the labels; keep (A). Choice (B) says that it will take 75 months to pay off the loan, but 75 is multiplied by the number of months. This is not consistent with the labels, so eliminate (B). Choice (C) states that 75 is the rate of increase in the total amount owed, but 75 × months since the loan was made is subtracted from, not added to, the amount owed. Eliminate (C). Choice (D) states that 75 is the rate of increase in the monthly payments, but again, there is not an increase because the equation features subtraction. Eliminate (D). The correct answer is (A).