Average price per person I am having trouble judging where I am going wrong with the following question


The price of lunch for 15 people was $207.00 including a 15% gratuity for service.What was the average price per person EXCLUDING the gratuity ?
    a)11.73 b)12.00 c)13.80 d)14.00 (Ans=12.00)


Here is how I am solving it
Without tip = $207-\frac{15}{207} = 175.93$ 
Per Person = $\frac{175.95}{15} = 11.73$
Why is my answer wrong ?

Let $x$ be the total bill, without tip. Then the bill with tip is $x$ plus $15\%$ of $x$. So it is $x(1.15)$.
Thus $x(1.15)=207$. Now you can find $x$, and divide by $15$.
The above is probably the most natural way to solve the problem. One could alternately say that the amount paid per person is $\frac{207}{15}=13.80$. If $y$ is the bill per person before tip, then $y(1.15)=13.80$. 
Remark: To see that the procedure you used is not correct, suppose that the bill before tip is $100$. Then the tip will be $15$, so the bill after tip is $115$. What happens if you remove $15\%$ of this? You end up below $100$.
