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 7 cubic feet and the volume of each large box is 20 cubic feet. There were 8 more small boxes shipped than large boxes and the total volume of all boxes was 245 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
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 7 cubic feet and the volume of each large box is 20 cubic feet. There were 8 more small boxes shipped than large boxes and the total volume of all boxes was 245 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
Solution
Let's denote the number of large boxes shipped as and the number of small boxes shipped as .
From the problem, we have the following information:
- The volume of each small box is 7 cubic feet.
- The volume of each large box is 20 cubic feet.
- There were 8 more small boxes shipped than large boxes.
- The total volume of all boxes was 245 cubic feet.
We can set up the following equations based on this information:
- (since there were 8 more small boxes than large boxes)
- (since the total volume of all boxes was 245 cubic feet)
Now, we can substitute the first equation into the second equation to solve for :
Expanding the equation:
Combining like terms:
Subtracting 56 from both sides:
Dividing both sides by 27:
Now that we have , we can find using the first equation:
Therefore, the number of small boxes shipped is 15 and the number of large boxes shipped is 7.
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