Write system of equation from context

Question

Write System of Equations from Context

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 22 cubic feet. There were 2 more small boxes shipped than large boxes and the total volume of all boxes was 320 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.

I need

Let __=_______________________

Let __=_______________________

and

The Systems of Equations

____________________

____________________

Answer 1

x = number of small boxes, y = number of large

x = y + 2

6x + 22y = 320

You can solve by plotting on Desmos or a graphing calculator and seeing where they intersect

Answer 2

Hello, Bob,

Let L = number of large boxes

Let S = number of small boxes

We know that S = L + 2

We also know total volume is 320 ft³

Total volume is the number of small boxes times 6 ft³ plus the number of large boxes at 22 ft³.

Therefore: S*6 + L*22 = 320

Substitute the other equation for S to get (L+2)*6 + L*22 = 320

6L + 12 + 22L = 320

28L = 308

L = 11, therefore S = 13

11*22 = 242 and 13*6 = 78 for a total of 320 ft³.

Bob