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I know 8,000 represents 40% of X and I'd like to figure out X.

I can start by doubling 8,000 and that gets me 80% of the total.

10% of the 8,000 is 1,000 and I can add that twice to get the remaining 20%.

If 8,000 is 40% of X, then X is 18,000.

Is that right?

user21820
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    You're almost right. Just some correction, $10%$ is $2000$ so you would have $20,000$ as final answer – Azlif Nov 04 '19 at 10:44
  • Like always in math problems, mark $x=$ the unknown number. You know that $8~000$ represents $40~%$ of an unknown number, that is ("40 per cent of an unknown number is 4000") $$ 0.4 x = 8~000 $$ Now it should be a lot clearer. – Matti P. Nov 04 '19 at 10:46
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    The easiest way is to divide by $0.4$ , as Matti explained. – Peter Nov 04 '19 at 10:47
  • If $8000$ is a $40$% of $X$, then $8000/X=0.4$. From here you can find $X$. Or you can reason like this: write under each other $8000-40$%, $X-100$% and do the cross multiplication. After that, you would be able to find $X$. – user13 Nov 04 '19 at 10:48

4 Answers4

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$8,000$ is $40\%$ of the whole

Divide by $4$

$2,000$ is $10\%$ of the whole

Muliptly by $10$

$20,000$ is $100\%$ of the whole.

This answer doesn't really depend on algebra (but essentially the same) , using just your head. But, like other answers suggest, mastering algebra would help you better to solve another problem.

Azlif
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No. Note that $40\%$ of $X$ just means $0.4X$, and so $0.4X=8000$. Dividing by $0.4$ yields $X=20000$.

Your mistake was that if $8000$ is $40\%$, then $10\%$ is $2000$.

Generally, the first approach is preferable, because it'd work with any percentage.

Yuval Gat
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This can be done with basic algebra.

Remember 40% $= \frac{40}{100}$

We are saying what number times 40% gives us $8000$,

$$8000=x\frac{40}{100}$$

$$800000=40x$$

$$20000=x$$

PMaynard
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If: $$ \begin{split} 40\% &= 0.4\\ 8000 &\to 0.4\\ x &\to 1 \end{split} $$ then: $$ x = \frac{8000 \cdot 1 }{0.4} = \frac{8000}{0.4} = 20000 $$

Daniele Tampieri
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Duarte Castanho
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