SOLUTION: In the period of a year, an investor lost twice as much as he gained. If he originally had $10,000 , and he now has 8,000, what amount did he gain and what amount did he lose.

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Question 196226: In the period of a year, an investor lost twice as much as he gained. If he originally had $10,000 , and he now has 8,000, what amount did he gain and what amount did he lose.
My daughter and I have been working ont his but I am quite sure that we are not getting the right answer and we are totally stumped!
I hope someone can help!!!!
She is thinking gain of 2000 and loss of 4000- that seems wrong but who knows...
I think our minds are blown at this point
Please Help!!
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

She is exactly correct. Here's why:

Let x represent the amount gained, then 2x is the amount lost. So he started with 10K added x and then subtracted 2x leaving him with 8K, or:








John

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let g= the amount he gained
Then 2g will be the amount he lost
given:
10000+%2B+g+-+2g+=+8000
10000+-+g+=+8000
-g+=+-+2000
g+=+2000
2g+=+4000
He gained $2,000 and lost $4,000
check:
10000+%2B+2000+-+4000+=+8000
12000+-+4000+=+8000
8000+=+8000
OK - I think your daughter was right