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January 12th, 2017, 04:10 PM   #1
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Finding the total number if I have a %

Hi,

I know it's on Khan Academy but not sure what the specific word is for my question to find it. If you have a problem where you know 111 is 32% of a number, how do you find the number? (I don't care about that specific number, but in general how you solve problems like that.) I know I've done it before and it was a lot easier than I thought but for some reason it escapes me.

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Last edited by blimper; January 12th, 2017 at 04:11 PM. Reason: change example
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January 12th, 2017, 04:27 PM   #2
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$a = p \% \text{ of } b$

$a = \dfrac{p}{100}b$

$\dfrac{100 a}{p} = b$

$111 = 32 \% \text{ of } b$

$b = \dfrac{11100}{32} = 346.875$
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January 12th, 2017, 05:08 PM   #3
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Thank you!
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January 12th, 2017, 05:22 PM   #4
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$111$ $\color{red}{is}$ $\color{blue}{\text{32%}}$ of a $\color{green}{number}$

$111$ $\color{red}{=}$ $\color{blue}{0.32}(\color{green}{number})$

$\dfrac{111}{\color{blue}{0.32}} \color{red}{=} \color{green}{number}$
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January 13th, 2017, 07:39 AM   #5
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Quote:
Originally Posted by blimper View Post
I know it's on Khan Academy but not sure what the specific word is for my question to find it.
A Google video (or youtube) search for Percent word problem finds KA's laboriously worked example (numbered 5) and others. Note that such videos tend to work a particular example (or examples) without explaining the general mathematical principles involved. Also, they tend not to tell you how to verify that your answer is correct, and don't tell you the commonest mistakes that are made when doing such problems.
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January 13th, 2017, 12:50 PM   #6
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Quote:
Originally Posted by blimper View Post
If you have a problem where you know 111 is 32% of a number, how do you find the number?
32% of "that number" WAS calculated:
n * .32 = 111
So calculating n is a no-brainer, right?

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January 23rd, 2017, 01:58 AM   #7
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It's a simple problem, let the $x$ and make proportion.

$111$ is $32\%$ of $x$

$\dfrac{111}{x}=\dfrac{32}{100}$

$32x=11100$

$x=\dfrac{11100}{32}$

$x=346.875$
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January 24th, 2017, 02:40 AM   #8
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Quote:
Originally Posted by blimper View Post
Hi,

I know it's on Khan Academy but not sure what the specific word is for my question to find it. If you have a problem where you know 111 is 32% of a number, how do you find the number? (I don't care about that specific number, but in general how you solve problems like that.) I know I've done it before and it was a lot easier than I thought but for some reason it escapes me.

Thanks.
The answer is 355. You multiply 111 by 32 % then move the decimal over one slot when you get 35.52
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January 24th, 2017, 03:31 AM   #9
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It's necessary to divide (not multiply) 111 by .32, as already explained.
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January 25th, 2017, 06:21 PM   #10
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Quote:
Originally Posted by blimper View Post
Hi,

I know it's on Khan Academy but not sure what the specific word is for my question to find it. If you have a problem where you know 111 is 32% of a number, how do you find the number? (I don't care about that specific number, but in general how you solve problems like that.) I know I've done it before and it was a lot easier than I thought but for some reason it escapes me.

Thanks.
Divide by 32, then multiply by 100. I do think that memorizing formulas are harder than doing it automatically.
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