Question

a library loans out 3 books every day for a week and no books are returned. the equation below is written to represent the situation: (-3)·7 = -21 which description best explains the meaning of -21 in the equation? a books were loaned out for -21 days. b the library now has -21 books. c the change in the number of books at the library over the course of the week was -21. d the number of books loaned per day was -21.

Explanation:

• Option A: Days cannot be negative in this context. The number of days is 7 (a positive value), so this option is incorrect.
• Option B: The number of books in a library cannot be negative in a practical sense. The negative sign here represents a decrease, not a negative quantity of books. So this option is wrong.
• Option C: Since 3 books are loaned out each day (a decrease of 3, represented as - 3) and this happens for 7 days, the total change in the number of books (calculated as \((-3)\times7=-21\)) is a decrease of 21. This option is correct.
• Option D: The number of books loaned per day is 3 (represented as - 3 in the equation to show a decrease), not - 21. So this option is incorrect.

Answer:

C. The change in the number of books at the library over the course of the week was \(-21\).