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Here is an example:

24.30 + 66.6% = 40.50
40.50 - 60% = 24.30
or (24.30 + 66.6%) - 60% = 24.30

I know if I add $66.6\%$ to $24.30$, I get $40.50$ and if I subtract $60\%$ from $40.50$ I get the other value back (values are being rounded here!)

$$(X + Y\%) - Z\% = X$$

My variable is $60\%$ ($Z\%$). Is there a way to derive $Y\%$ from that, so I don't have to calculate it ($Y\%$) by hand each time ?

Thanks!

mathematics2x2life
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    If user127001 gives you an apparently wrong result, then it is because you have mislead them: Indeed 24.3 is 60% of 40.5, it is not 40.5 “minus 60%”. – Carsten S Jan 20 '14 at 00:44
  • Extremely unclear as to what is meant. Tried twice, deleted my answers. Did you ride the bus, or did you bring your lunch? – MPW Jan 20 '14 at 05:14
  • I probably should have said i needed a simple explanation cause i had a hard time following all those cute algebra tables. The only answer that got me tilting is when user127001 said ..well, it's the "inverse of 0.40" ..ding ! Ok, that's easy ! So yeah, downvote the question all you like guys (not talking to you MPW ..unless you did) it's one thing to give an answer, but another to give it in a way that someone who hasn't been eating math for breakfast everyday can understand. Especially when the answer was as simple as just saying ..Y% is the inverse of Z% - 1 –  Jan 21 '14 at 00:54

2 Answers2

1

Your notation is a bit deceptive.

What you obviously mean instead of Adding 60% to X is Adding 60% **of X** to X which means the same as Multiply X by 1,60

In your concrete example you want to add Y% of X to X, and afterwars you want to substract 60% of this result from this result.

You have to find Y such that $$ X\cdot Y \cdot \left(1-0.60\right) = X\cdot Y \cdot 0.40 = X $$ which means that Y has to be the inverse of $0.40$ which is equal to 2.50

The result means, that you have to add $2.50-1.00=1.50 = 150$% of X to X in the first step.

user127.0.0.1
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  • Took me a while to grasp but this works perfectly. The inverse of the number to substract = the number that was added: Y% = ((((1 / Z%) * 100) - 1) * 100) –  Jan 20 '14 at 01:29
1

Let's start with the fact the percentage are not magic numbers, no need to express it with %.. they are just numbers. $60\%$ means $\frac{60}{100} = 0.6$

Saying "add 60 % only means that, taken any number $x$, the resulting number will be

$$x + 60\% \ x = x + 0.6x = x(1 + 0.6) = 1.6x = z$$

In the general case, an increment of $b$ means $x(1+b) = z$

Now you want to find a number such that

$$z - az = z(1 - a) = x$$ Since $x = \frac{z}{1+b}$, you can write $$z(1-a) = \frac{z}{1+b} \Rightarrow a = \frac{b}{1+b}$$

for example if $b = 40\% = 0.4$, and $x = 40.25$, we have

$40.25 + 40\% (40.25) = 56.36$; From the formula above we get $a = \frac{0.4}{1.4} = 0.2857 = 28.57\%$

And in fact $56.36 - 28.57\% (56.36) = 40.25$

Ant
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