a fruit company delivers its fruit in two types of boxes: large and small. a delivery of 2 large boxes and 3 small boxes has a total weight of 78 kilograms. a delivery of 6 large boxes and 5 small boxes has a total weight of 180 kilograms. how much does each type of box weigh ?
weight of each large box: ? kilogram(s)
weight of each small box: ? kilogram(s)

The information given in the problem statement lets you write two equations relating box weights (L for the large box weight; S for the small box weight).

2L +3S = 78 . . . . . . weight of the first collection of boxes

6L +5S = 180 . . . . . weight of the second collection of boxes

We can subtract 3S from the first equation and multiply it by 3 and we have ...

2L = 78 -3S . . . . . . subtract 3S [eq3]

6L = 234 -9S . . . . . multiply by 3

Now we have an expression for 6L that can substitute into the second equation:

(234 -9S) +5S = 180

234 -4S = 180 . . . . . . . . simplify

54 -4S = 0 . . . . . . . . . . . subtract 180

13.5 -S = 0 . . . . . . . . . . . divide by 4

13.5 = S . . . . . . . . . . . . . add S

From [eq3] above, we can now find L.

2L = 78 -3(13.5) = 37.5

L = 37.5/2 = 18.75

The weight of the large box is 18.75 kg; the small box is 13.5 kg.

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A graphing calculator can provide an alternate means o finding the solution.