SOLUTION: A buyer for a toy store wanted the wholesaler to deliver as many scarce toy bears as possible. However, the buyer wanted twice as many brown bears as black bears and half as many

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Question 919369: A buyer for a toy store wanted the wholesaler to deliver as many scarce toy bears as possible. However, the buyer wanted twice as many brown bears as black bears and half as many white bears as black bears. The supplier delivered a truck load of 1,288 bears. How many bears of each color should have been delivered?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of brown bears
Let +b+ = number of black bears
Let +c+ = number of white bears
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(1) +a+=+2b+
(2) +c+=+%281%2F2%29%2Ab+
(3) +a+%2B+b+%2B+c+=+1288+
-----------------------
Substitute (1) and (2) into (3)
(3) +2b+%2B+b+%2B+%281%2F2%29%2Ab+=+1288+
(3) +%28+6%2F2+%29%2Ab+%2B+%281%2F2+%29%2Ab+=+1288+
(3) +%28+7%2F2+%29%2Ab+=+1288+
(3) +7b+=+2576+
(3) +b+=+368+
and
(1) +a+=+2b+
(1) +a+=+2%2A368+
(1) +a+=+736+
and
(2) +c+=+%281%2F2%29%2Ab+
(2) +c+=+%28+1%2F2+%29%2A368+
(2) +c+=184+
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736 = number of brown bears
368 = number of black bears
184 = number of white bears
--------------------------
check:
(3) +a+%2B+b+%2B+c+=+1288+
(3) +736+%2B+368+%2B+184+=+1288+
(3) +1288+=+1288+
OK