Math Problem. Stuck Help

Question

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 22 cubic feet. A total of 22 boxes of paper were shipped with a combined volume of 324 cubic feet. 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

S + L = 22 (not surprisingly S=number of Small boxes, L= number of Large boxes)

6S + 22L = 324 ft^3

multiply 1st equation by 6

6S + 6L = 6(22) = 132 ft^3

subtract last equation from 2nd equation to get

22L - 6L = 16L = 324- 132

L = 192/16

L = 12 Large boxes

S =22-12 = 10 Small boxes

check the answer:

6(10) +22(12) = 60+264 = 324