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March 25th, 2015, 07:17 PM   #1
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How to Calculate the amount if you know the total and percentage

Hello newbie here.

Long story short looking for a crash course on Algebra, its been a while since I geared my brain up for math, but I have taken up to Statistics, let me know if you guys know of any online Algebra course?

here is what I currently have in mind.

If I know a percentage increase of an amount, how do I figure how much the number was increased by.

The dollar amount is 19,244 and percentage increase is 63.2, how do I calculate how much X was increased by to get to dollar of 19,244?

Last edited by dado123; March 25th, 2015 at 07:24 PM.
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March 25th, 2015, 07:25 PM   #2
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Math Focus: Calculus/ODEs
If $X$ is the original amount, and we increase it by 63.2% and get 19244, then we may write:

$\displaystyle 1.632X=19244$

Hence:

$\displaystyle X=\frac{19244}{1.632}=\frac{35375}{3}= 11791.\overline{6}$

And so the increase in $X$ is:

$\displaystyle \Delta X=19244-\frac{35375}{3}=\frac{22357}{3}=7452.\overline{3}$
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March 25th, 2015, 07:30 PM   #3
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Thanks, can you please expand on how the percentage of 63.2 when to be written as 1.632?
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March 25th, 2015, 07:42 PM   #4
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If we take some quantity $X$ and increase if by 63.2%, we are adding to $X$ a quantity that is equal to 63.2% of $X$:

$\displaystyle X+63.2\%\cdot X$

Now, the percentage symbol is shorthand for $\displaystyle \frac{1}{100}$ as it means per (for each) centum (100), and when we divide by 100, we move the decimal point two places to the left, so we have:

$\displaystyle X+0.632X$

Now, we may factor out $X$ since it is a common factor in both terms:

$\displaystyle X(1+0.632)$

Combining the two numbers and putting them in front of the variable as is traditional and allowed by the commutativity of multiplication (this just means $a$ times $b$ is the same as $b$ times $a$), we have:

$\displaystyle 1.632X$

Does this make sense?
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