Amount- Pounds

[Guest]

Raisins are packed in 3 sizes of boxes- small, medium, large.

3 small and 2 large hold 55 lbs.

2 medium and 4 small hold 50 lbs.

1 large and 3 medium hold 65 lbs.

Determine pounds 1 box of each size holds.


My partial attempt:

Let S = small
Let M = medium
Let L = large

3S + 2L = 55

2M + 4S = 50

1L + 3M = 65

How do I proceed from here ?

[Guest]

You are on the right track.

The last equation tells you that 1L = 65-3M, you can substitute that into the first equation to get
3S+2(65-3M) = 55
which simplifies to
3S+130-6M = 55
which rearranges to
3S = 6M-75
dividing both sides by 3 gives
S = 2M-25

Substituting it into the second equation gives
2M+4(2M-25)=50
which goes to
2M+8M-100 = 50
or
10M = 150
so M=15.
It is easy to then calculate that S = 5 and L = 20.

Hope this helped,

R. Baber.

[Guest]

That helps. Thanks.