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.

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

The number of small boxes shipped are 14 and the number of large boxes shipped are 7.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, the volume of each small box is 6 cubic feet and the volume of each large box is 12 cubic feet.

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

There were twice as many small boxes shipped as large boxes

So, x=2y ------(I)

The total volume of all boxes was 168 cubic feet.

6x+12y=168 ------(II)

Substitute equation (I) in equation (II), we get

6(2y)+12y=168

12y+12y=168

24y=168

y=7

Substitute y=7 in equation (I), we get

x=14

Therefore, the number of small boxes shipped are 14 and the number of large boxes shipped are 7.

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

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