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 10 cubic feet and the volume of each large box is 20 cubic feet. There were twice as many small boxes shipped as large boxes shipped and the total volume of all boxes was 240 cubic feet. Graphically solve a system of equations in order to determine the number of small boxes shipped,

x
,
x, and the number of large boxes shipped,
y
y.
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 10 cubic feet and the volume of each large box is 20 cubic feet. There were twice as many small boxes shipped as large boxes shipped and the total volume of all boxes was 240 cubic feet. Graphically solve a system of equations in order to determine the number of small boxes shipped,
x
,
x, and the number of large boxes shipped,
y
y.

Answer 1

(x, y) = (12, 6)

Explanation:

The problem is solved much more easily by considering groups of 2 small and 1 large boxes. Such a group will have a volume of 2·10+20 = 40 ft³, so 240/40 = 6 such groups are needed.

The number of small boxes shipped is 6·2 = 12; the number of large boxes shipped is 6.

_____

To solve this graphically, we must write two equations in x and y:

x = 2y . . . . . the number of small boxes is twice the number of large boxes

10x +20y = 240 . . . . the total volume is 240 ft³

The attached graph shows the solution of these equations.

(x, y) = (12, 6)