A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 7 large boxes and 9 small boxes has a total weight of 192 kilograms. A delivery of 5 large boxes and 3 small boxes has a total weight of 114 kilograms. How much does each type of box weigh?
Let's denote the weight of a large box as L and the weight of a small box as S.
From the given information, we can create the following system of equations:
7L + 9S = 192
5L + 3S = 114
Now, we can solve this system of equations using either substitution or elimination method.
Using the elimination method, we can multiply the first equation by 3 and the second equation by 9 to make the coefficients of S the same:
21L + 27S = 576
45L + 27S = 1026
Now, subtract the second equation from the first equation:
24L = 450
L = 450 / 24
L = 18.75
Now, we can substitute the value of L back into one of the original equations to solve for S:
5(18.75) + 3S = 114
93.75 + 3S = 114
3S = 20.25
S = 20.25 / 3
S = 6.75
Therefore, the large boxes weigh 18.75 kg each and the small boxes weigh 6.75 kg each.