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I'm totally confused, we were doing a question in class and there are two answers but I'm not sure why one works and the other one doesn't.

For example; there are 6000 pandas now and over 10 years they have decreased by 40%. How many pandas were there 10 years ago? There are two methods that I have found.

Method 1. 10% of 6000 is 600 x 4 = 2400 + 6000 = 8400 pandas.

Method 2. 6000 = 60% devide by 3 = 2000 x 5 = 10000 pandas.

Then though 40% of 8400 is 3360 which if you take off 8400 isn't 6000.

But if you use method two it works.

Why is this? I mean how come one method works and the other doesn't?

I know this is pretty easy but I just really want to know, thanks.

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    $\begingroup$ With Method 1 you are calculating 40% of the current pandas. Since those 6000 pandas represent 60% of the original, the 2400 are 40% of the 60%, so 24% of the original amount. $\endgroup$
    – SinisterMJ
    Commented Sep 21, 2013 at 14:28

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In Method 1, you calculated $40\%$ of the number of pandas NOW. Since those 6000 pandas represent 60% of the original, you calculated $40 \%$ of $60\%$, that is: 24% of the original amount.

In method $2$, you correctly calculated what the original number of pandas must be if $60\%$ of that original number reduces the number to $6000$ now existing pandas.

In short, we're given that $6000$ is the number of pandas that remain after a $40\%$ decrease in the original number of pandas $(x)$ ten years ago. In math, we can write this as

Let $x = \text{the number of pandas 10 years ago}$. We know that $40\% x = \dfrac{40}{100} x = 0.4x$.

$$x - 0.4 \cdot x = 6000 \iff 0.6 x = 6000$$

Solving for $x$ gives us that there were $x = \dfrac {6000}{0.6} = 10,000 \,\text{ pandas 10 years ago}$.

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