Comments on: How do I solve for a percentage of a total budget...
http://ask.metafilter.com/272786/How-do-I-solve-for-a-percentage-of-a-total-budget/
Comments on Ask MetaFilter post How do I solve for a percentage of a total budget...Tue, 09 Dec 2014 15:46:28 -0800Tue, 09 Dec 2014 15:50:47 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: How do I solve for a percentage of a total budget...
http://ask.metafilter.com/272786/How-do-I-solve-for-a-percentage-of-a-total-budget
This will be easy for someone, but math is my second language so I'm at a loss.
How do I solve for the percentage of a TOTAL budget, when one line item is unknown (and is part of the total budget)? <br /><br /> Specifically, I have a budget with 20 line items. I know the value of all the line items, except for one, and that one unknown value has to equal 16.5% of the TOTAL budget. How do I figure this out? Without that line item to start with, I don't have the total budget - does this question make sense?<br>
<br>
Bonus if you can tell me what formula to plug into Excel so that I never have to think about this again.<br>
<br>
Thanks so much!post:ask.metafilter.com,2014:site.272786Tue, 09 Dec 2014 15:46:28 -0800coollibrarianmathbudgetsexcelformularesolvedBy: Admiral Haddock
http://ask.metafilter.com/272786/How-do-I-solve-for-a-percentage-of-a-total-budget#3959249
Take the sum of all the values you have and divide that number by .835. That's the total budget. The total number times .165 is the missing value.comment:ask.metafilter.com,2014:site.272786-3959249Tue, 09 Dec 2014 15:50:47 -0800Admiral HaddockBy: Admiral Haddock
http://ask.metafilter.com/272786/How-do-I-solve-for-a-percentage-of-a-total-budget#3959253
Or in Excel <br>
=(((sum(a1:a19))/.835))*.165<br>
<br>
Filling in a1:a19 with the relevant cells (assuming they're contiguous).comment:ask.metafilter.com,2014:site.272786-3959253Tue, 09 Dec 2014 15:56:20 -0800Admiral HaddockBy: DanSachs
http://ask.metafilter.com/272786/How-do-I-solve-for-a-percentage-of-a-total-budget#3959297
To explain why Admiral Haddock is correct: your nineteen items are 83.5% of the total budget.comment:ask.metafilter.com,2014:site.272786-3959297Tue, 09 Dec 2014 16:46:19 -0800DanSachsBy: axiom
http://ask.metafilter.com/272786/How-do-I-solve-for-a-percentage-of-a-total-budget#3959369
If you want to <strike>torture yourself</strike> see what a formal explanation of this looks like (for any number of values):<br>
<br>
Let c<sub>i</sub> represent the cost of item <i>i</i> and express percentages as values between 0 and 1 (16.5 percent is equal to .165, for example -- just divide the percentage by 100 to get the appropriate value between 0 and 1). We have <i>n</i> total items (in your example, n=20). Let <i>B</i> represent the total budget. Let <i>w</i> be the weight (percentage of total budget) corresponding to whichever item <i>k</i> has the unknown cost. We know the following facts:<br>
<br>
B = c<sub>1</sub> + c<sub>2</sub> + ... + c<sub>n</sub><br>
w * B = c<sub>k</sub><br>
<br>
Subtracting c<sub>k</sub> from both sides of the first equation gets us:<br>
<br>
B - c<sub>k</sub> = c<sub>1</sub> + c<sub>2</sub> + ... + c<sub>k-1</sub> + c<sub>k</sub> + c<sub>k+1</sub> + ... + c<sub>n</sub> - c<sub>k</sub><br>
<br>
The c<sub>k</sub> values on the right-hand side cancel, and I can rewrite c<sub>k</sub> on the left as (w * B) due to the second equation above:<br>
<br>
B - (w * B) = c<sub>2</sub> + ... + c<sub>k-1</sub> + c<sub>k+1</sub> + ... + c<sub>n</sub><br>
<br>
We know all the values on the right-hand side, so let's call their sum <i>T</i>. This gets us (here I'm writing (1 * B) explicitly to make the next step clearer):<br>
<br>
(1 * B) - (w * B) = T<br>
<br>
Factor out the B on the left gives us:<br>
<br>
(1 - w) * B = T<br>
<br>
Divide both sides by (1 - w):<br>
<br>
B = T / (1 - w)<br>
<br>
Now everything on the right is a known quantity. Plug in the appropriate values and you can calculate B. Once you know B, you can plug in all the known values in the first equation at the top to get c<sub>k</sub>.comment:ask.metafilter.com,2014:site.272786-3959369Tue, 09 Dec 2014 18:11:04 -0800axiomBy: coollibrarian
http://ask.metafilter.com/272786/How-do-I-solve-for-a-percentage-of-a-total-budget#3959477
Thank you, everyone! <br>
Wow, I am not smart. I actually needed ALL of that explanation, lol.comment:ask.metafilter.com,2014:site.272786-3959477Tue, 09 Dec 2014 20:12:11 -0800coollibrarian