A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 45 books. There were twice as many large boxes sent as small boxes, which altogether can hold 440 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.

Question

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 45 books. There were twice as many large boxes sent as small boxes, which altogether can hold 440 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.

Answer 1

Let's define the variables:

Let s be the number of small boxes sent.
Let l be the number of large boxes sent.

We can write two equations based on the given information:

1) Each small box can hold 20 books, so the total number of books in small boxes would be 20s.
2) Each large box can hold 45 books, so the total number of books in large boxes would be 45l.

The total number of books sent is given as 440:
20s + 45l = 440

We are also given that there are twice as many large boxes sent as small boxes:
l = 2s

Therefore, the system of equations that could be used to determine the number of small boxes sent (s) and the number of large boxes sent (l) is:
20s + 45l = 440
l = 2s