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 8 cubic feet and the volume of each large box is 23 cubic feet. There were 2 more small boxes shipped than large boxes and the total volume of all boxes was 171 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
number of large boxes --- x
number of small boxes = x+2
23x + 8(x+2) = 171
solve for x to unravel the mysteries of the boxes.
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 80 pounds. A total of 19 boxes of paper were shipped weighing 1280 pounds altogether. Determine the number of small boxes shipped and the number of large boxes shipped.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the number of small boxes shipped is S, and the number of large boxes shipped is L.
According to the problem, the volume of each small box is 8 cubic feet, so the total volume of all small boxes is 8S cubic feet.
Similarly, the volume of each large box is 23 cubic feet, so the total volume of all large boxes is 23L cubic feet.
The problem also states that there were 2 more small boxes shipped than large boxes, so we can express this as an equation: S = L + 2.
Finally, the total volume of all the boxes is given as 171 cubic feet, so we have the equation: 8S + 23L = 171.
Now we have a system of equations with two unknowns, S and L. We can solve these equations simultaneously to find the values of S and L.
Using the equation S = L + 2, we can substitute this expression into the other equation:
8(L + 2) + 23L = 171.
Distributing the 8, we have:
8L + 16 + 23L = 171.
Combining like terms, we get:
31L + 16 = 171.
Subtracting 16 from both sides of the equation, we have:
31L = 155.
Dividing by 31, we find:
L = 5.
Substituting this value back into the equation S = L + 2, we have:
S = 5 + 2 = 7.
So, the number of small boxes shipped is 7, and the number of large boxes shipped is 5.