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January 12th, 2017, 04:10 PM  #1 
Member Joined: Mar 2016 From: NJ Posts: 48 Thanks: 2  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. Thanks. Last edited by blimper; January 12th, 2017 at 04:11 PM. Reason: change example 
January 12th, 2017, 04:27 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,463 Thanks: 1340 
$a = p \% \text{ of } b$ $a = \dfrac{p}{100}b$ $\dfrac{100 a}{p} = b$ $111 = 32 \% \text{ of } b$ $b = \dfrac{11100}{32} = 346.875$ 
January 12th, 2017, 05:08 PM  #3 
Member Joined: Mar 2016 From: NJ Posts: 48 Thanks: 2 
Thank you!

January 12th, 2017, 05:22 PM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,947 Thanks: 1555 
$111$ $\color{red}{is}$ $\color{blue}{\text{32%}}$ of a $\color{green}{number}$ $111$ $\color{red}{=}$ $\color{blue}{0.32}(\color{green}{number})$ $\dfrac{111}{\color{blue}{0.32}} \color{red}{=} \color{green}{number}$ 
January 13th, 2017, 07:39 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133  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.

January 13th, 2017, 12:50 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,594 Thanks: 1038  
January 23rd, 2017, 01:58 AM  #7 
Member Joined: Sep 2016 From: India Posts: 88 Thanks: 30 
It's a simple problem, let the $x$ and make proportion. $111$ is $32\%$ of $x$ $\dfrac{111}{x}=\dfrac{32}{100}$ $32x=11100$ $x=\dfrac{11100}{32}$ $x=346.875$ 
January 24th, 2017, 02:40 AM  #8  
Banned Camp Joined: Nov 2016 From: St. Louis, Missouri Posts: 28 Thanks: 4 Math Focus: arithmetic, fractions  Quote:
 
January 24th, 2017, 03:31 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
It's necessary to divide (not multiply) 111 by .32, as already explained.

January 25th, 2017, 06:21 PM  #10  
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  Quote:
 

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