SOLUTION: In the period of a year, an investor lost twice as much as he gained. If he originally had $10,000 and now has $6000, what amount did he gain and what did he lose?

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Question 306959: In the period of a year, an investor lost twice as much as he gained. If he originally had $10,000 and now has $6000, what amount did he gain and what did he lose?
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say he gained X dollars and then lost 2X dollars.
10000+X=2X=6000
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: X=4000.
  • Graphical form: Equation 10000%2BX-2X=6000 was fully solved.
  • Text form: 10000+X-2X=6000 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+10000%2BX-2X=6000+%29
    For tutors: simplify_cartoon( 10000+X-2X=6000 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+10000+%29%2BX-2%2AX=6000.
Moved 10000 to the right of expression
It becomes X-2%2AX%2Bhighlight_green%28+10000+%29=6000.
Look at highlight_red%28+X+%29-highlight_red%28+2%2AX+%29%2B10000=6000.
Eliminated similar terms highlight_red%28+X+%29,highlight_red%28+-2%2AX+%29 replacing them with highlight_green%28+%281-2%29%2AX+%29
It becomes highlight_green%28+%281-2%29%2AX+%29%2B10000=6000.
Look at %28highlight_red%28+1+%29-highlight_red%28+2+%29%29%2AX%2B10000=6000.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2AX%2B10000=6000.
Look at %28highlight_red%28+-1+%29%29%2AX%2B10000=6000.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2AX%2B10000=6000.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2AX+%29%2B10000=6000.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2AX%2B10000=6000.
Look at -highlight_red%28+1+%29%2AX%2B10000=6000.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -X%2B10000=6000.
Look at -X%2B10000=highlight_red%28+6000+%29.
Moved these terms to the left highlight_green%28+-6000+%29
It becomes -X%2B10000-highlight_green%28+6000+%29=0.
Look at -X%2Bhighlight_red%28+10000+%29-highlight_red%28+6000+%29=0.
Added fractions or integers together
It becomes -X%2Bhighlight_green%28+4000+%29=0.
Look at highlight_red%28+-X%2B4000+%29=0.
Solved linear equation highlight_red%28+-X%2B4000=0+%29 equivalent to -X+4000 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: X=4000.

Universal Simplifier and Solver


Done!