Difference between revisions of "2017 AMC 8 Problems/Problem 17"
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Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have? | Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have? | ||
− | <math>\textbf{(A) }9\qquad\textbf{(B) }27\qquad\textbf{(C) }45\qquad{(D) }63\qquad\textbf{(E) }81</math> | + | <math>\textbf{(A) }9\qquad\textbf{(B) }27\qquad\textbf{(C) }45\qquad\textbf{(D) }63\qquad\textbf{(E) }81</math> |
==Solution== | ==Solution== |
Revision as of 08:15, 31 March 2018
Problem 17
Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 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
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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All AJHSME/AMC 8 Problems and Solutions |
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