If I end up with $10,000 because I lost 20% in 2 years...

Question

If I end up with 10,000 after losing 20% in two years...How much did I have in the first place?

Answer 1

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

$$\frac{80}{100}x=\$10,000$$

Answer 2

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$.

Answer 3

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