A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 35 pounds and each large box of paper weighs 60 pounds. There were 7 more small boxes shipped than large boxes and the total weight of all boxes was 815 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.

Question

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 35 pounds and each large box of paper weighs 60 pounds. There were 7 more small boxes shipped than large boxes and the total weight of all boxes was 815 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.

Answer 1

Let's denote the number of small boxes as S and the number of large boxes as L.

From the problem, we know that each small box weighs 35 pounds and each large box weighs 60 pounds.

The first equation we can write is the relationship between the number of small boxes and the number of large boxes: S = L + 7.

The second equation we can write is the relationship between the total weight of all boxes and the weight of each box: 35S + 60L = 815.

Therefore, the system of equations is:

S = L + 7
35S + 60L = 815