Reverse Engineering Percentage Problem

[FlyingEagle]

Hi all,

I tried the search function and Google, but can't find anything helpful. Unfortunately my time in school is long ago, so I hope you can help me.

I have a problem that I know the Input Value and the Percentage it will have been increased.

concrete example:

Input Value = 340,000
Percent = 13.81%
Output Value = 394,500 (this has to be calculated in the future)

So you see, that I don't have the absolute percentage increase. I need to go 394,500 - 13.81% = 340,000 (ignore the rounding)

In the future I do not have the resulting value - I only have Input Value and Percentage available. This brings me to this formula that I need to resolve to x:

(x - 340,000) / x = 13.81%

And this is exactly where I'm failing since three days. How can I resolve this formula to fit?

Thanks for your advice - I hope you understand my problem

 

[lookagain]

I need to go 394,500 - 13.81% = 340,000 (ignore the rounding)

You need to multiply the percent (rate) by the amount before you subtract it from the amount:

394,500 - (13.81%)(394,500) = 340,000 (roughly)

 

[Dr.Peterson]

Input Value = 340,000
Percent = 13.81%
Output Value = 394,500 (this has to be calculated in the future)

So you see, that I don't have the absolute percentage increase. I need to go 394,500 - 13.81% = 340,000 (ignore the rounding)

In the future I do not have the resulting value - I only have Input Value and Percentage available. This brings me to this formula that I need to resolve to x:

(x - 340,000) / x = 13.81%

And this is exactly where I'm failing since three days. How can I resolve this formula to fit?

Thanks for your advice - I hope you understand my problem

You're right that 394,500 reduced by 13.81% is 394,500(1 - 0.1381) = 340,019.55.

But that is a percent decrease from 394,500, not a percent increase as you said at the start, "I know the Input Value and the Percentage it will have been increased."

If you start from 340,000 and increase by 13.81%, the result will be 340,000(1 + 0.1381) = 386,954.

The equation you show is for reversing a percent decrease to result in 340,000. If that is what you want, you can solve the equation:

(x - 340,000) / x = 13.81%​

(x - 340,000) / x = 0.1381​

x - 340,000 = 0.1381x​

x - 0.1381x = 340,000​

0.8619x = 340,000​

x = 340,000/0.8619 = 394,477.32​

Check: a 13.81% decrease from 394,477.32 is 394,477.32(1 - 0.1381) = 339,960.55, which is about right. Note that this is a simple formula: 340,000/(1 - 0.1381), which reverses the first line I wrote.

Can you clarify what you need to do?

 

[Otis]

Output Value = 394,500 (this has to be calculated in the future)

(x - 340,000) / x = 13.81%

Hi FlyingEagle. That equation looks similar to the Percent-Change Formula, with one change:

(x - 340000)/340000 = 13.81%

If x is the new value, and 340000 is the old value, then the percent-change going from 340000 to x is given by:

(New - Old)/Old = Percent Change (in decimal form)

Solving (x - 340000)/340000 = 0.1381 for x gives x=386954.

In other words, the percent-change going from 340,000 to 386,954 is 13.81%.

Check: (386954 - 340000)/340000 = 0.1381

Is that what you're trying to do? (If so, let us know if you'd like help with the steps solving for x.)



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