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 50 pounds and each large box of paper weighs 80 pounds. There were 4 more large boxes shipped than small boxes and the total weight of all boxes was 1750 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 assume that the number of small boxes shipped is represented by the variable 'S' and the number of large boxes shipped is represented by the variable 'L'.

According to the given information, the paper company shipped 4 more large boxes than small boxes. Therefore, the number of large boxes shipped can be expressed as:

L = S + 4

The total weight of all boxes shipped is 1750 pounds. Since each small box weighs 50 pounds and each large box weighs 80 pounds, we can calculate the total weight using the following equation:

50S + 80L = 1750

So, the system of equations can be written as:

L = S + 4
50S + 80L = 1750

To write the system of equations, let's define the variables as follows:

Let "s" represent the number of small boxes shipped.
Let "l" represent the number of large boxes shipped.

Now, let's define the equations based on the given information:

1) "There were 4 more large boxes shipped than small boxes":
We can express this as l = s + 4, since the number of large boxes is 4 more than the number of small boxes.

2) "The total weight of all boxes was 1750 pounds":
We can express this as the sum of the weights of small and large boxes, which can be calculated by multiplying the number of boxes by their respective weights. So, the equation becomes:
50s + 80l = 1750

Therefore, the system of equations is:
l = s + 4
50s + 80l = 1750

These equations can be used to determine the number of small and large boxes shipped by solving the system.

s = small boxes , g = large boxes

g = s + 4

80 g + 50 s = 1750

Step-by-step explanation:

Let x be the number of small boxes and let y be the number of large boxes

According to the first statement, a total of 21 boxes were shipped
Equation 1 will be:
x+y=21

According to 2nd statement, the total weight was 1110 and we know the weight of one small box is 25 and large box is 70
Equation 2 will be:
25x+70y=1110

Use the substitution method for solving the equation

Putting the value of x in equation 2
25(21-y) +70y =1110
525-25y+70y = 1110
45y = 585
Y=13

Putting the value of y in equation 1
x+13 = 21
X = 8

Number of small boxes shipped = 8
Number of large boxes shipped = 13