Expert: Scott A Wilson - 9/29/2009

Question

While on vacation, Talisha won a lot of tickets at two arcades on the boardwalk she was
visiting. The first arcade charges $1 to cash in the tickets and gives you 12 cents back on each ticket won, while the second arcade gives you 10 cents back on each ticket and no fee to cash in. In order for  Talisha  to make an equal profit from each arcade, how many tickets must she have won?  

Answer
Since I gives 12c profit and II gives 10c profit,
start with 1.  10c is not divisible by 12, neither is 20, neither is 30, neither is 40,
neither is 50, but 60 is.  60 = 5*12 and 60 = 6*10.

Another way of doing this was to note that the prime facotrs of 12 are 2, 2, and 3 and
the prime factors of 10 are 2 and 5.  Putting these together means the prime factors must be
2, 2, 3, and 5.  2*2=4, 4*3=12, 12*5=60.

I don't see where it says anything about how much money she had,
but to make the winnings equal, she could have both a few or many.
What she won, then, was 5n 12c tickes and 6n 10c tickets for some value of n.
It could have been 5 and 6, 10 and 12, 15 and 18, etc.