Question

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds and each large box of paper weighs 100 pounds. A total of 20 boxes of paper were shipped weighing 1400 pounds altogether. Graphically solve a system of equations in order to determine the number of small boxes shipped,x, and the number of large boxes shipped, y. please include graph.

Answer 1

12 small boxes

8 large boxes

Explanation:

let x be the number of small boxes shipped

let y be the number of large boxes shipped

This means:

the total number of boxes is 20, so

x + y = 20

the number of 50 pound boxes is x and the number of 100 pound boxes is y and together there are 1400 pounds, so

50x + 100y = 1400

Then, solve

First, simplify the equation 50x + 100y = 1400 by dividing both sides by 50

x + 2y = 28

Now, subtract the two equations:

x + 2y = 28

- (x + y = 20)

y = 8

Now plug this into the equation x + y = 20

x + 8 = 20

x = 12

So the number of small boxes is 12 and the number of large boxes is 8.

Here's a graph: