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# Figuring out percentage

Posted on 2006-05-04
Medium Priority
14,614 Views
Hello All:

I have a problem I need to figure out for my job.

Say I have an amount (\$100.00).  I need to know what amount I need to add to it so that whenI take 40% from the new total, I get \$100.00.

This would need to work no matter what % I use, so I guess I'm looking for a formula  in the way of

x + y = (x + y)/ 40%

I think I need to know what y would be.

Thanks for any help I can get with this.

jocasio
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Question by:Juan Ocasio
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LVL 143

Assisted Solution

Guy Hengel [angelIII / a3] earned 300 total points
ID: 16609960
simply:

\$100 is 60% of the value you are looking for, hence

x = \$100 / 60 * 100 = 500/3 = 166,666666...
check: 40% of 166,666 = 66,66666...

so, you have to add 2/3 to \$100%, which is 66,666666%
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LVL 85

Assisted Solution

ozo earned 300 total points
ID: 16610100
Why would anyone assign a job that takes longer to assign than to do?
This sounds more like homework for school.
(100 + x)*(1 - 40/100) = 100
x = 100/(1-40/100) - 100

0

LVL 15

Author Comment

ID: 16611362
ozo:
I wish I was still young enough to be in school :)  Actually, I work in an office that gets commissions off of monies we collect.  It was 40% which was nice and easy; we collect money and then we take 40% off for commission.  One of our new clients did not like this arrangement so they wanted us to add a fee to their collectible amount.  Because our commission is 40%, we needed to figure our how much to charge so that when 40% comes off the top, our client gets 100% of their collectible.  So that's the story in a nut shell..

angellIII:
So this will work with any other values, say our % is 33.33, I would do the following:

100/66.67*100 ?

ozo:  would I substitute 33.33 for the 40 in your equation?

Thanks,

jocasio
0

LVL 85

Expert Comment

ID: 16611390
(100 + x)*(1 - 33.33/100) = 100
x = 100/(1-33.33/100) - 100
0

LVL 3

Expert Comment

ID: 16612420
If you take 40% which sjould be 100 so

40% is 100
means
100% is 250

result you have to add 150....
0

LVL 3

Expert Comment

ID: 16612434
Formula wise
prev value = 100

total (100 + y)

40% of (100 + y) = 100

40(100 + y)/100 = 100

2(100 + y)/5 = 100
200 + 2y = 500

2y = 500 - 200

2y= 300

y = 150
0

LVL 3

Expert Comment

ID: 16612450
I guess angelll, ozo and jocasio123 are confused with language and intrepreted wrong..
OR
I have interpreted wrong...

>>whenI take 40% from the new total,
>>I get \$100.00.

i interpret that 40% of new value is 100...

0

LVL 85

Expert Comment

ID: 16612460
There seems to be an ambiguity in what "whenI take 40% from the new total, I get \$100.00." means
Do you get the 40%, or do you get what is left after the 40% is taken?
0

LVL 3

Expert Comment

ID: 16612468
Previous Value = X

Total become (X + Y)

P% of new value is Z

then formula will be

P*(X + Y)/100 = Z;

Here
X = 100
Z = 100
P = 40

40*(100 + Y)/100 = 100;

==>  Y = 150

0

LVL 3

Expert Comment

ID: 16612476
I guess....What ever you take....That you will get...

Not take out our left out....so does not seems abiguity but seems mis intrepretation which is almost impossible from ozo.....
0

LVL 17

Expert Comment

ID: 16612825
Be aware that you will get rounding errors - the occasional penny will be lost as you are rounding to currency values.
I had to do something similar once to work out pre-taxed amounts when given only the full billed amounts. Summing all these valuse and adding tax at the correct percentage rarely came to exactly the same result. Not you can do about it apart from deciding in whose favour the error will be made.

0

LVL 44

Accepted Solution

Arthur_Wood earned 400 total points
ID: 16613615
let X = old value and Y = new value

X = 100

y - 40% * Y  = 100

.6 Y = 100 ===> Y = 166.66

In order for your company to get their expected 40% commision, and the customer to get his expected \$100 , you should charge \$166.66

in general, if your percentage is P  then the formalau would read

Y = X/(1-P)   so if P = .33 (33%)  Y = X/(.67) ===>  Y = 1.5 * X

AW
0

LVL 15

Author Comment

ID: 16613943
All Thanks for the help.  I will award the points as follows:

Authur Wood for supplying a very concise formula 100 pts

AngelIII and ozo for also helping 75 pts each

Thanks again...
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