SOLUTION: Hi jane and john had some marbles. After jane gave john some marbles, he had 3 times as many as he had at first. Jane then hsd half the number of marbles that john had. If they ha

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Question 1105169: Hi
jane and john had some marbles. After jane gave john some marbles, he had 3 times as many as he had at first. Jane then hsd half the number of marbles that john had. If they had a total of 180 marbles, how many did each have at first.
Thanks
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
At first, jane had x marbles and john had y marbles.
The exchange of marbles from jane to john was m marbles.

The description can be turned into system of equations according to the description:
system%28x%2By=180%2Cy%2Bm=3y%2Cx-m=%281%2F2%29%2A3y%29

system%28m=2y%2Cy=2x-3m%2Cx%2By=180%29

substitute for m,
system%28x%2By=180%2C2x=7y%29

highlight%28y=40%29------------john had originally
-
highlight%28x=140%29-----------jane had at first