PSAT Math Multiple-Choice Question 144: Answer and Explanation

Question: 144

Sydney borrowed money from a friend and is paying back the loan. The remaining amount she owes, A, can be calculated by the equation A = 870 - 30w, where w represents the number of weeks since she took the loan. What does the number 870 represent?

• A. The total amount of money Sydney has repaid
• B. The amount of money Sydney repays each week
• C. The number of weeks Sydney has been paying back the loan
• D. The original amount that Sydney borrowed

Correct Answer: D

Explanation:

D

The question asks for the meaning of a piece of an equation in context. Start by reading the full question, which asks for the meaning of the number 870. Then label the parts of the equation with the information given. The question states that A represents the remaining amount she owes and w represents the number of weeks since she borrowed the money. Because the number 870 is used to calculate A, the remaining amount owed, it must have something to do with money. Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) describes the total amount Sydney has repaid. However, the amount will change over time, so it cannot be represented by a constant. Eliminate (A). Choice (C) describes w and not 870, so eliminate (C). To check (B) and (D), plug in some numbers. If w = 1, then A = 870 - 30(1) = 840, so after 1 week, $840 remains to be paid. If w = 2, then A = 870 - 30(2) = 810, so after 2 weeks, $810 remains to be paid. Therefore, between week 1 and week 2, 840 - 810 = 30 was repaid. Thus, 30 represents the amount Sydney repays each week, so eliminate (B). Only one choice remains. To confirm (D), note that the original amount that Sydney owes is the amount that she owes after 0 weeks. If w = 0, then A = 870 - 30(0) = 870. The correct answer is (D).