Word problems with missing parts

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 6 cubic feet and the volume of each large box is 13 cubic feet. A total of 19 boxes of paper were shipped with a combined volume of 156 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.

Answer 1

Let the number of small boxes shipped be x, and the number of large boxes shipped be y.

We are given the following information:

1. Each small box has a volume of 6 cubic feet.
2. Each large box has a volume of 13 cubic feet.
3. A total of 19 boxes were shipped, so: x + y = 19
4. The total volume of the shipment was 156 cubic feet, so: 6x + 13y = 156

We have 2 equations, 2 unknowns:

x + y = 19

6x + 13y = 156

Now, we can solve these two equations simultaneously using substitution or elimination. I will use substitution for illustration purposes:

x + y = 19

x = 19 - y

Substitute the x equation into the x in the 2nd equation:

6(19 - y) + 13y = 156

114 - 6y + 13y = 156

7y = 42

y = 6

Remember that x = 19 - y:

x = 19 - (6) = 13

So, x, the number of small boxes, is 13, and y, the number of large boxes, is 6.