Answer:
- large box: 18.75 kg
- small box: 13.5 kg
Step-by-step explanation:
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.
_____
A graphing calculator can provide an alternate means o finding the solution.
