If I end up with 10,000 after losing 20% in two years...How much did I have in the first place?
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20 percent per year for two years or twenty percent total over the course of two years? – 123 Sep 04 '14 at 01:10
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20% total over the course of two years – user173640 Sep 04 '14 at 01:10
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If you lost $20\%$, then you only have $80\%$ of your original value left. If you started with $x$ dollars, then an appropriate equation for you to solve is
$$\frac{80}{100}x=\$10,000$$
user137794
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You had $X$ to begin with.
Then, after two years, since you lost $20 \%$, you had $80 \%$ left. That $80 \%$ that is left is $ \$10,000$. But this is also $.8X$ (eighty percent of what you started with).
So we get $.8X = 10,000$. Solving for $X$ gives:
$X = \frac{10000}{.8} = 12500$
So, you started with $ \$12,500$.
layman
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@user173640 Great! If you find one answer you've received is better than the others, and answers your question, then you should click the check mark next to it to accept it. But if you want to wait for more answers, that's ok too! – layman Sep 04 '14 at 01:14
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If you mean you lost twenty percent per year for two years:
$x-.2x-.2(x-.2x)=10000$
$.8x-.2(.8x)=10000$
$(80/100)x - (16/100)x = 10000$
$64x/100 = 10000$
$64x = 1000000$
x = 15625
If you lost twenty percent total:
$.8x=10000$
x=12500
123
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