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:
$(-3)\cdot7=-21$
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 cannot be negative in this context. The number of days is 7 (a positive value).
• Option B: The library can't have a negative number of books in a real - world sense. The negative sign here represents a decrease, not a negative count of books.
• Option C: Since 3 books are loaned out each day (a decrease of 3 per day, represented as $-3$) and this happens for 7 days, the total change in the number of books (using the formula $(-3)\times7=-21$) is a decrease of 21. So, the change in the number of books at the library over the week is $-21$.
• Option D: The number of books loaned per day is 3, not $-21$. The $-3$ in the equation represents the rate of decrease (3 books loaned out per day).

Answer:

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