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 13 cubic feet. A total of 26 boxes of paper were shipped with a combined volume of 254 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
There were
small boxes shipped and
large boxes shipped.
S+L = 26
7S + 13L = 254
Now solve for S and L.
To determine the number of small and large boxes that were shipped, we can use a system of equations.
Let's assume the number of small boxes shipped is 'x' and the number of large boxes shipped is 'y'.
According to the information given in the question, the volume of each small box is 7 cubic feet, and the volume of each large box is 13 cubic feet.
We are also given that a total of 26 boxes of paper were shipped, so we can write the equation:
x + y = 26 ---(Equation 1)
The combined volume of all the boxes is 254 cubic feet. Since the volume of each small box is 7 cubic feet and the volume of each large box is 13 cubic feet, we can write the second equation:
7x + 13y = 254 ---(Equation 2)
Now, we have a system of equations consisting of equation 1 and equation 2. We can solve this system of equations to find the values of x and y.
One way to solve this system of equations is by substitution or elimination. Let's use the elimination method.
Multiply equation 1 by -7 to make the coefficients of x in both equations equal:
-7x - 7y = -182 ---(Equation 3)
Now, add equation 3 and equation 2 to eliminate x:
(-7x + 7x) + (-7y + 13y) = -182 + 254
6y = 72
Divide both sides of the equation by 6:
y = 12
Substitute the value of y in equation 1:
x + 12 = 26
x = 26 - 12
x = 14
Therefore, the number of small boxes shipped is 14 and the number of large boxes shipped is 12.
So, there were 14 small boxes shipped and 12 large boxes shipped.