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.
Let's denote the number of small boxes shipped as "x" and the number of large boxes shipped as "y".
From the problem, we know that each small box weighs 35 pounds and each large box weighs 60 pounds. Therefore, the total weight of the small boxes is 35x pounds and the total weight of the large boxes is 60y pounds.
According to the problem, there were 7 more small boxes shipped than large boxes. We can express this as: x = y + 7.
The total weight of all boxes is 815 pounds, so we can write the equation: 35x + 60y = 815.
Therefore, the system of equations is:
x = y + 7
35x + 60y = 815.
In this system, x represents the number of small boxes shipped and y represents the number of large boxes shipped.