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 7 cubic feet and the volume of each large box is 13 cubic feet. There were twice as many large boxes shipped as small boxes shipped and the total volume of all boxes was 165 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.

Answer 1

small boxes = 5 and large boxes = 10

Explanation:

Given:

The volume of each small box is 7 cubic feet.

volume of each large box is 13 cubic fee.

There were twice as many large boxes shipped as small boxes shipped.

Total volume of all boxes was 165 cubic feet.

Question asked:

The number of small boxes shipped and the number of large boxes shipped?

Solution:

Let number of small boxes shipped = x

Then, the number of large boxes shipped = 2x (given)

Total volume of all boxes = 165 cubic feet.

no. of small boxes
`*` vol. of each small box + no. of large boxes
`*` vol. of each large box = 165 cubic feet. (Total volume of all boxes)

`x *7 + 2x * 13 = 165\\7x + 26x = 165\\33x = 165`

Dividing both side by 33

`x = (165)/(33)\\ x = 5`

The number of small boxes shipped =
`x` = 5

The number of large boxes shipped = 2
`x` = 2
`*` 5 = 10