# Math Help - Percentage Discount Problem

1. ## Percentage Discount Problem

So,

I take 10% off a line of products (in my online store) via a php script. The prices of the parts were not the same to start with.

Now I need to add the 10% back across the line of products. If I do that it obviously fails.

$100 - 10% = 90$
$90 + 10% = 99$

99$is not equal to the original$100 price.

So yeah, is there anything I can do to get back to normal pricing?

Thanks for help.
Tai

2. Hi

Originally Posted by taikahn
So,

I take 10% off a line of products (in my online store) via a php script. The prices of the parts were not the same to start with.

Now I need to add the 10% back across the line of products. If I do that it obviously fails.

$100 - 10% = 90$
$90 + 10% = 99$

99$is not equal to the original$100 price.

So yeah, is there anything I can do to get back to normal pricing?
Of course there is

Your original price is x;

x - 0.1*x = cheaper products

(e.g. 100 - 0.1*100 = 90)

-------

now you know, your product costs \$90 = cheaper product

x - 0.1*x = cheaper products

<=>
x (1-0.1) = cheaper products

x (0.9) = cheaper products

x = cheaper products / 0.9

(e .g. cheaper product = 90

->x = 90/0.9 = 100)

I hope this helps,
Rapha

3. ## add 11.1111111%

add 11.1111111111%

4. Originally Posted by rick_rine@yahoo.com
add 11.1111111111%
This is certainly a practical if all the OP wants to do is get the price back without worrying about why this works.

But it might be helpful to add some backstory to it:

Let the original price be x.

Discount price: x - (10% of x) = x - 0.1 x = 0.9 x.

You want to add a percentage of the discount price to get the original price back. Consider:

0.9 x + (a % of (0.9)x) = x

$\Rightarrow 0.9 x + \frac{a}{100} \cdot (0.9 x) = x$

$\Rightarrow 0.9 + \frac{0.9 a}{100} = 1$

$\Rightarrow \frac{0.9 a}{100} = 0.1$

$\Rightarrow a = \frac{10}{0.9} = \frac{100}{9} = 11 \frac{1}{9}$

So add $11 \frac{1}{9}$%

5. ## Ours is not to reason why

Thanks mate. Your right that it is very important to understand why we do what we do in maths. It is logical and not simply a set of rules.
Thanks
Rick

6. If 90 + x% of 90 = 100
x/100 * 90 =10
so, x = 100/9
So, we get 90+ 11.111111% of 90 = 100

We must remember that x% of y = y% of x i.e 9% of 10 = 10% of 9 and;10% of 9 != 9 % of 10