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 18 cubic feet. A total of 27 boxes of paper were shipped with a combined volume of 342 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
Answer
Let x be the number of small boxes shipped.
The volume of the small boxes is 6x cubic feet.
The number of large boxes shipped is 27 - x.
The volume of the large boxes is 18(27 - x) cubic feet.
The total volume is 6x + 18(27 - x) = 342.
Simplifying the equation, we get:
6x + 486 - 18x = 342
-12x = -144
x = 12
So, 12 small boxes were shipped and 27 - 12 = 15 large boxes were shipped.