SOLUTION: I need explanation and solution: A store divides 112 kilograms of potatoes into 3 kilogram and 2 kilogram bags. If the store ends up with twice as many 2 kilogram bags as 3 kilogr

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Question 861356: I need explanation and solution:
A store divides 112 kilograms of potatoes into 3 kilogram and 2 kilogram bags. If the store ends up with twice as many 2 kilogram bags as 3 kilogram bags, find how many bags of each type the store starts with.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 3 kg bags used
Let +b+ = number of 2 kg bags used
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(1) +3a+%2B+2b+=+112+
(2) +b+=+2a+
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By substitution:
(1) +3a+%2B+2%2A%28+2a+%29+=+112+
(1) +7a+=+112+
(1) +a+=+16+
and, since
(2) +b+=+2a+
(2) +b+=+32+
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There are 16 of the 3 kg bags and
32 of the 2 kg bags