PSAT Math Multiple-Choice Question 629: Answer and Explanation

Question: 629

A library fines a patron who fails to return a book on time the replacement cost of the book plus an additional 10 cents each day that the fine is not paid in full. On December 1, Jane borrowed a book with a replacement cost of $30. The book was due to be returned on December 14. Which function models the total amount of dollars (A ) that Jane will need to pay x days after December 14?

• A. A (x) = 30 + 10x
• B. A (x) = 30 + 0.1x
• C. A (x) = 30 + 1.4x
• D. A (x) = 30 - x

Correct Answer: B

Explanation:

(B) The book will have a fixed replacement cost of $30, so +30 will be a constant term in the function. For each day that the book goes unreturned past December 14, Jane owes another 10 cents. Thus on day 1 after the return date, she owes a $30 replacement fee and 10 more cents, for a total of $30.10. On the second day, she owes the $30 replacement fee and 2 days' worth of late fees, (2)(10) = 20 cents, for a total of $30.20. By continuing in this manner, on day x, Jane will owe the $30 replacement fee and x days' worth of late fees, which is (x)(10) = 10x cents or 0.1x dollars. The total cost is shown by A(x) = 30 + 0.1x.

This relationship is best described in choice (B).

Choice (A) is tempting, but you must remember that 10 cents is expressed in dollars as $0.10. Choice (A) instead indicates that Jane pays an additional $10 of fees every day plus the $30 replacement fee.