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I'm a simple man who doesn't know much math. Sometimes in my work and life I've to do math calculations. Today was one of those days and I've spent the last hour trying to figure this out.

Look. Let's say the old pricing of a set of screwdrivers was \$228. I want to sell them for a new price of \$199. What is the discount that I apply?

I'm using various methods to find it, but I've no idea what I'm doing and which is the right way.

Method 1

I divide the discount \$29 by the old price:

$$\frac{228-199}{228}$$

I get 13% off.

Method 2

I divide the discount \$29 by the new price:

$$\frac{228-199}{199}$$

I get 15% off.

Method 3

I divide the new price \$199 by the old price \$228

$$\frac{199}{228}$$

I get 13% off.

Method 4

I divide the discount \$29 by the old:

$$\frac{228-199}{228}$$

I get 13% off.

So the discount is either 13% or 15%. Which is it and which is the right method?

bodacydo
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  • 3
    Your method 1 is identical to method 4. – The Artist Dec 15 '14 at 09:20
  • In method 3, the fraction you show is (about) $87%$. Presumably you are subtracting it from $100%$ to get $13%$. Once you do that, it is the same as method 1 and 4 (which are truly identical). – Ross Millikan Jun 12 '15 at 04:42

4 Answers4

3

You would normally (probably always) measure a discount as a fraction of the original price. In your example, 13%

If we measure the discount as a fraction of the new price, the discount could be more than 100% which doesn't sound right. (Old price \$100, new price \$50. You would probably agree that this is a 50% discount, not a 100%.)

mrf
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Methods 1 and 4 (have you noticed?) are identical, and both are correct.

A discount is always written as a percentage of the original price. If the original price is A and the new price is B, then the discount = 1 - B / A. This is equivalent to your methods 1, 3, and 4.

For example:
A = 100
B = 25
Discount = 1 - (25 / 100) = 1 - 1/4 = .75, or 75%.

Joanna Marietti
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The original price is 228\$, the new price is 199\$. Therefore, the discount is 29\$ in absolute terms.

Measured again by the original price (the one you are giving a discount on), the relative discount is

$$\frac{29$}{228$}\times 100\% \approx 12.7\% $$

which I feel is fair to round up to $13\%$ for the purposes of advertising (beware, though, that laws may apply which say otherwise).

The general method to calculate the relative (percentage) discount on the original price is to divide the absolute discount by the original price (after all, you are giving "X % off the original price").

0

How to calculate what percentage of 228 is 199?

Algebra simplifies the question. Let the percentage be $x$. Now, ask $what~\%$ of Original Price (228) is equal to the discounted price. Assign a variable (say $x$) to this. Therefore: $$\frac{x}{100}\times 228 = 199$$ $$x=\frac{199\times 100}{228}=87.28\%$$

To find discount %, you can let discount % be $y$ and proceed similarly : $$\frac{y}{100}\times228=228-199=29$$ $$y=\frac{2900}{228}=12.719\%$$