Solve System of Equations from Content

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

Let B = number of SMALLER boxes

Let 2B = number of LARGER boxes, since twice as many large boxes shipped than smaller boxes

7B + (2)(13)B = 165 (SMALLER box=7 cu ft and LARGER box=13 cu ft.)

7B + 26B = 165

33B = 165

B = 5 (Dividing both sides by 33.)

Therefore, 5 SMALL boxes were shipped and 10 LARGE boxes were shipped(2x5).

CHECKING:

5 small boxes X 7 cu ft = 35 cu ft

10 large boxes X 13 cu ft = 130 cu ft

130 cu ft + 35 cu ft = 165 cu ft