This equation is very difficult for me and i need help with it?

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 45 pounds and each large box of paper weighs 75 pounds. There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 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

The unknowns are the # of small boxes and the # of large boxes. You can use S to represent the # of small boxes and L to represent the # of large boxes in your equations.

Anytime you have a word problem, you need to look for something (a quantity) that you can set equal to another quantity. This problem gives you a total (the total weight of all boxes). This can be set equal to the sum of all the boxes' weights. You know that 45 lbs times the number of small boxes will equal the weight of all the small boxes and 75 lbs times the number of large boxes will equal the weight of all the large boxes. So, the total weight of all boxes has to equal 45S + 75L:

1455 = 45S + 75L

To solve for 2 variables you need 2 equations. The problem also states that there are 3 more small boxes than large boxes. So, you can write an equation stating that the number of small boxes equals

the number of large boxes plus 3:

S = L + 3

Now, you can solve this system of equations by substituting (L+3) for S in the first equation:

1455 = 45(L+3) + 75L

Next, solve for L:

1455 = 45L + 135 + 75L

1320 = 120L

L = 11

Finally, solve for S by substituting 11 for L in either equation:

S = 11 + 3