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Q: Business math: 3 simple % formulas ( Answered,   0 Comments )
Subject: Business math: 3 simple % formulas
Category: Miscellaneous
Asked by: tobes-ga
List Price: $15.00
Posted: 05 Dec 2004 12:36 PST
Expires: 04 Jan 2005 12:36 PST
Question ID: 438448
1. I know that a number is 7.75% of a larger number. What is a simple
formula to find the larger number?
2. I know what  I paid for an item. I know what I want my mark-up % to
be. What is the simple formula to find the selling price?
3. I know what something is selling for and I know what I paid for it.
What is the simple formula to find what the mark-up % is?
Subject: Re: Business math: 3 simple % formulas
Answered By: mathtalk-ga on 05 Dec 2004 18:56 PST
Hi, tobes-ga:

First a couple of things to keep in mind about percentages.  A
percentage is a pure number, a fraction expressed as "parts per
hundred" (per cent).  7.75% is the same as 0.0775, for example.

Also, when we speak of one thing being a certain percentage of some
value, the word "of" means times.  So $5 is 50% of $10 means simply:

  $5 = 0.50 * $10

1.  If we know that a number X is 7.75% of a larger number Y, that means:

   X = 0.0775 * Y

To find what Y is when X is known, we should divide X by 0.0775:

   Y = X / 0.0775

For example, if the smaller number is X = 15.50, and you divide it by
0.0775, you find the larger number is Y = 15.50/0.775 = 200.

We often refer to the amount that the percentage is taken "of" as the
"base", which is Y in this case.

2. Suppose you paid Y for an item, and you know what "mark-up"
percentage you like to have.  Since the mark-up is an additional
amount, added to the amount to paid to get the selling price,  we
would write the selling price S as:

   S = Y + (p*Y) = (1 + p) * Y

where p is the mark-up percentage.

For example, if you want the mark-up to be 10% = 0.10, you would
multiply the amount you paid Y by 1 + 0.10:

  S = 1.10 * Y

to get the selling price S.

3.  When you know what something is selling for, S, and also what was
the amount paid for it , Y, then the same formula can be "solved" to
find the mark-up:

  S = (1 + p) * Y

  1 + p = S / Y

  p = (S / Y) - 1 = (S - Y)/Y

That is, the mark-up is the difference S - Y between selling price and
amount paid, divided by the base (amount paid).

For example, if a lamp is sold for $124 that you paid only $80 for, we
would say the mark-up was:

  p = (124 - 80)/80 = 44/80 = 0.55 = 55%

Note that if the selling price S were less than the amount you paid Y,
then the mark-up would be a negative number!  In this case we usually
turn the difference around and refer to the percentage as a mark-down,
but either way the amount paid Y is the "base" of the percentage.

Please let me know if further clarification would be helpful.

regards, mathtalk-ga
There are no comments at this time.

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