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:

Step1: Analyze each option

• Option A: Days can't be negative in this context. Loaning books for $-21$ days is not meaningful.
• Option B: The library can't have a negative number of books in a practical sense. The value $-21$ represents a change, not the actual number of books.
• Option C: Since 3 books are loaned out each day (a decrease, so $- 3$ per day) and there are 7 days, the total change is $(-3)\times7=-21$. This means the number of books at the library decreased by 21 over the week.
• Option D: The number of books loaned per day is $-3$ (negative because it's a decrease), not $-21$.

Answer:

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