Answer:
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 12 cubic feet. There were twice as many small boxes shipped as large boxes shipped and the total volume of all boxes was 168 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.
\underline{\text{Define Variables:}}
Define Variables:
May choose any letters.
\text{Let }s=
Let s=
\,\,\text{the number of small boxes shipped}
the number of small boxes shipped
\text{Let }l=
Let l=
\,\,\text{the number of large boxes shipped}
the number of large boxes shipped
Each small box has a volume of 6 cubic feet, so the volume of ss small boxes would be 6s6s cubic feet. Each large box has a volume of 12 cubic feet, so the volume of ll large boxes would be 12l12l cubic feet. Therefore, the total volume 6s+12l6s+12l equals 168:168:
6s+12l=168
6s+12l=168
Since there were twice as many small boxes shipped as large boxes, there were more small boxes, so if we multiply 2 by the number of large boxes, we will get the number of small boxes, meaning ss equals 2l.2l.
let s = number of small boxes shipped
let l= number of large boxes shipped
6s+121 = 168
s=21
