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.
give two systems of equations
Let's define the variables for the system of equations:
Let S = number of small boxes
Let L = number of large boxes
System of equations 1:
1. Each small box can hold 20 books:
20S = total number of books in small boxes
2. Each large box can hold 45 books:
45L = total number of books in large boxes
3. There were twice as many large boxes sent as small boxes:
L = 2S
4. Altogether, the boxes can hold 440 books:
20S + 45L = 440
System of equations 2:
1. Each small box can hold 20 books:
20S = total number of books in small boxes
2. Each large box can hold 45 books:
45L = total number of books in large boxes
3. There were twice as many large boxes sent as small boxes:
L = 2S
4. The total number of boxes is unknown but can be represented by T:
T = total number of boxes
5. Each small box and large box contribute to the total number of boxes:
S + L = T