2017 AMC 8 Problems/Problem 17
Problem 17
Starting with some gold coins and some empty treasure chests, I tried to put gold coins in each treasure chest, but that left
treasure chests empty. So instead I put
gold coins in each treasure chest, but then I had
gold coins left over. How many gold coins did I have?
Solution
We can represent the amount of gold with and the amount of chests with
. We can use the problem to make the following equations:
Therefore, This implies that
We therefore have
So, our answer is