Calculating a the % of a number to give you a desired result

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December 21st 2009, 10:38 AM
Aloupha

Calculating a the % of a number to give you a desired result

Hello,

I am trying to come up with a formula (or use an existing one) to calculate a certain percentage (known) of an unknown number to give a known result.

For example, a problem might come in this form: 2.9% of this number is equal to 675. What is the number?

Any ideas?

Edit: Sorry, I just noticed I posted this in the wrong forum. (I misread Calculator for Calculation). Please delete!
December 21st 2009, 12:32 PM
pickslides

Hi there Aloupha

Your problem

Quote:

Originally Posted by Aloupha

For example, a problem might come in this form: 2.9% of this number is equal to 675. What is the number?

can be written as

$2.9\% \times x = 675$

as percent really means "out of 100" then

$\frac{2.9}{100} \times x = 675$

now solving for x you multiply both sides by 100 and divide both sides by 2.9

$x = \frac{675\times 100}{2.9}$

does this make sense?
December 22nd 2009, 06:41 AM
Aloupha

Thank you for your effort pickslides. While what you did did not solve what I seek, it helps me realize what I have been doing wrong. I have done what you suggested before and could not understand why I was not getting the result I was supposed to until I saw what you did (which I did - funny!).

I use paypal for online payment of a small business that I run. PayPal takes a 2.9% plus $0.30 fee off of every payment I receive. For the purpose of figuring out the formula, I decided to first work with the 2.9%. So I need to create a formula to calculate that 2.9% and add it as a processing fee to the client. That way, I will still get the target payment. So my question really is, what number I can take 2.9% off of it that will equal to 675.

$x-(\frac{2.9}{100}\times x)= 675$

So my formula would be:

$x-(\frac{2.9}{100}\times x)+0.30= y$

My math is rusty, is this accurate?
December 22nd 2009, 12:19 PM
pickslides

I totally understand the context of the proplem. My Girlfriend is a powerseller on EBay and uses Palpay in majority of her transactions.

Given this I am still a little unsure on what you are exactly trying to achieve. Let me guess.

You have a selling price in mind $x$ in dollars. You want to pass on the $2.9\%$ paypal fee to the seller therefore you need to inflate your selling price? I.e new selling price is $x+\frac{2.9x}{100} = 1.029\times x$
December 22nd 2009, 12:33 PM
Aloupha

I will have some set amounts depending on the package. Say I have 10 packages, each one will have a specific price.

Now, I do want to inflate the set price of any given package with the PayPal fee (2.9% + 0.30).

The billing invoice will look similar to this.

1. Package ------------------ $75.00
2. Processing Fee------------ The Value of 2.9%(of the overall price) + $0.30

Total (overal price)-------- The Value of 1 + 2

------------------------------------------------------
Working backwards, suppose I had the overall price and it was $75.00. PayPal would take 2.9%+0.30 off of the 75.00 and the remaining will be mine.

It will be like this:

1. Package 1 ---------------- $75.00
2. PayPal Fee -------------- $2.47

Balance --------------------- $72.52

Now, I do not want to be getting 72.52, I want my whole 75.00 dollars. So if I can figure out a way to compute the paypal fee when the I know the set price, I can charge my customers the set price + the paypal fee as opposed to just the set price.
December 22nd 2009, 12:42 PM
pickslides

In this case

Total $= \$75 + (.029\times \$75) +\$0.3 = \$77.48$
December 22nd 2009, 12:56 PM
Aloupha

Quote:

Originally Posted by pickslides

In this case

Total $= \$75 + (.029\times \$75) +\$0.3 = \$77.48$

Exactly! Now, I want to find the formula to calculate this.

It will be Y + (0.029 * Y) + 0.3 = X

Thanks!

Edit: wouldn't work :(
December 22nd 2009, 01:00 PM
pickslides

Ok, so let $x$ be the original price and $y$ be the inflated price then,

$y = 1.029x+0.3$
December 22nd 2009, 01:06 PM
Aloupha

How did you get the 1.029?
December 22nd 2009, 01:09 PM
pickslides

Quote:

Originally Posted by Aloupha

How did you get the 1.029?

from $y = x+0.029x+0.3$

$x+0.029x = 1.029x$

therefore $y = 1.029x+0.3$
December 22nd 2009, 01:16 PM
Aloupha

Quote:

Originally Posted by pickslides

from $y = x+0.029x+0.3$

$x+0.029x = 1.029x$

therefore $y = 1.029x+0.3$

Thanks, that definitely works! I can't believe it was this simple. I was complicating it.

I tested it against some transactions and it gets me very close (rounding issues).