Reverse my percentage?

December 6, 2009 7:25 PM

How do you find a number that minus a percentage of itself is a certain number?

What would be the formula (in a spreadsheet like pages.app) to find that 100 - 20% = 80, if you only know the percentage and the result (in this example 20% and 80)

I've tried googling this but I don't think I know the name or term of what I'm looking for, reverse percentage doesn't seem right...

posted by JulianDay to Education (7 answers total)

X * 0.8 = 80

X = 80 / 0.8
posted by mpls2 at 7:28 PM on December 6, 2009

Best answer: To be more precise...

X * (1 - 0.2) = 80

X = 80 / (1 - 0.2)
posted by mpls2 at 7:29 PM on December 6, 2009

Best answer: An easier way is to remember that subtracting a percentage is the same as multiplying by a fraction. In the case of 20%, that is 8/10 (x-20% = x * 8/10).

That makes the problem much easier to solve.

• x - 20% = 80
• 0.8x = 80
• x = 80 / 0.8

So the general formula is result/((100-percentage)/100)
posted by Deathalicious at 7:33 PM on December 6, 2009

Response by poster: Thanks so much.
posted by JulianDay at 7:33 PM on December 6, 2009

Use this to turn the word problem into an equation:
"of" is * (multiplication)
"is" is = (the equality sign)

Example:
$43 is 90% (10% off) of what?
43 = 0.90 * x
x = ...
posted by msittig at 7:41 PM on December 6, 2009

I was going to work it all out, but then just thought, hey, why not work it out as a normal algebraic statement and feed it to wolfram alpha.


http://www.wolframalpha.com/input/?i=x+-+%28x*%2820%2F100%29%29+%3D+80
posted by TravellingDen at 7:46 PM on December 6, 2009 [1 favorite]

I may have learned only one thing in middle school math, but it was this formula:

"Percent over 100 = 'is' over 'of'."

Cross multiply and divide to solve for the unknown.
posted by eafarris at 6:05 AM on December 7, 2009