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 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 1

Answer:

x is the number of large boxes shipped

y is the number of small boxes shipped

7 large boxes were shipped

14 small boxes were shipped

Step-by-step explanation:

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 : so if x large boxes , and y small boxes were shipped, then ,y =  2x small boxes were also shipped.

the total volume of all boxes was 168 cubic feet, which means:

y = 2x ...................(1)

6y + 12x = 168 .......(2),

then, replace y to 2x in the second equation

6(2x) + 12(x) = 168,

12x + 12x = 168,

24x = 168,

x = $\frac{168}{24}$ = 7,

since the small boxes = 2x,

2(7) = 14 boxes, so there are 14 small boxes being shipped,

and x = 7, so there are 7 large boxes being shipped, since x is the number of large boxes being shipped.