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number theory junior
Problem
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?
(A)
(B)
(C)
(D)
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: We do this because for 9 chests there are 2 empty and if 9 were in each 9 multiplied by 2 is 18 left. Therefore, This implies that We therefore have So, our answer is .
Final answer
C