SOLUTION: A 2-metre long wire is cut into 5 pieces. three of the shorter pieces have lenghts in cm, which are consecutive whole numbers while the two lnger pieces are each x cm. find the len

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Question 106390: A 2-metre long wire is cut into 5 pieces. three of the shorter pieces have lenghts in cm, which are consecutive whole numbers while the two lnger pieces are each x cm. find the lenght of the shortest piece.
Answer by josmiceli(6784) About Me  (Show Source):
You can put this solution on YOUR website!
The consecutive whole numbers can be called
n,n%2B1,n%2B2
The sum of the 2 longer pieces is 2x
What if each longer piece were 100 cm? Then ther would be nothing left for the
other three pieces
n+%2B+%28n%2B1%29+%2B+%28n%2B2%29+%2B+2%2A100+=+200
Now keep making x smaller and see how much is left for the other three
lengths, and if they can be consecutive numbers.
2x+=+198
1%2B2%2B3+=+6 and 6+%2B+198 is too big
2x+=+196
1%2B2%2B3+=+6 is still too big
2x+=+194
1%2B2%2B3+=+6 works out good
194+%2B+6+=+200
2x+=+194
x+=+97
So, the lengths are 1,2,3,97,97