Problem Solving

oxfordbound wrote:My issue is - how the hell do you simplify 207/1.15 fast enough?!?! At first I just did straight division which obviously took too long.

So far, my ideal solution has been to convert 1.15 to a fraction (23/20) and then break 207 into primes (23 and 9). I can cancel out the 23's and get 180, but this process seems extremely long winded.

That's the only way to simplify 207/1.15

However, you can choose not to simplify at that stage and continue as follows,
Total price of the lunch excluding gratuity = 207/1.1.5

Hence, average price of the lunch, excluding gratuity = 207/(1.15*15)

207/(1.15*15) = (207*100)/(115*15) = (9*23*100)/(5*23*3*5) = 3*4 = 12

It should be easy to note that 207 is divisible by 9 as sum of digits of 207 is divisible by 9.

Hope that helps.