How to get original number from percentages When I calculated $15\%$ of $150$ it's $22,5$. And than I do $150 - 22,5 = 127,5$.
Now I have number $127,5$ and I have $15\%$. 
How can I get from these two numbers ($127,5$ and $15\%$) back original number $150$?
Thank you a lot.
 A: This is what you did:
$$150-150\cdot 0.15=127.5$$
If you factorise, you obtain:
$$150(1-0.15)=127.5$$
Rearranging:
$$150=\frac{127.5}{1-0.15}=\frac{127.5}{0.85}$$
Hence, to obtain $150$, you must divide $127.5$ by $1-0.15$ ($100\text{%}-15\text{%}$), or $0.85$ ($85\text{%}$).
A: Percentages can be confusing.  For example, reduce 100 by 10% and you get 90.  Add 10% to 90 and you get 99.  You have not returned to where you started.  The reason is that although we talk of adding and subtracting percentages, we are really multiplying. Subtracting 10% actually means multiply by 90/100 = 0.9.  Adding 10% means multiply by 110/100 = 1.1.  Now, it is more obvious that the net effect of subtracting and adding 10% is to multiply by 0.99.  
So, to reverse a reduction by 10% you need to remember that it really means multiply by 0.9 so the reverse is to divide by 0.9 which is adding a little over 11%.  
A: Well, let's try to write the problem down more abstractly. To do so, instead of:
$$150-22.5=127.5$$ let us write $$150-(15\%) \cdot 150=127.5$$ Now if we convert percentages to decimals, we get:
$$150-(0.15) \cdot 150=127.5$$
Next up, we're going to do some algebraic trickery to the left side of the equation. In specific, we're going to divide by $150$ and multiply the sum we get by $150$ again. Let's make it less confusing in formula form: 
$$150-(0.15)\cdot150\rightarrow(1-0.15)\rightarrow 150\cdot(1-0.15)$$
We can do this because $$150-(0.15)\cdot150=150\cdot(1-0.15)$$
So now we've got:
$$150\cdot(1-0.15)=127.5$$ Therefore $$150=\frac{127.5}{(1-0.15)}$$
So if we buy an item in a shop that costs $\$35$ after a discount of $25\%$ has been applied, we can now calculate its original price (which we'll call $x$):
$$x=\frac{$35}{1-0.25}=\frac{$35}{0.75}=$46.67$$
