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Difference between revisions of "2017 AMC 8 Problems/Problem 17"

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==Problem 17==
 
==Problem 17==
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Starting with some gold coins and some empty treasure chests, I tried to put <math>9 </math> gold coins in each treasure chest, but that left <math>2</math> treasure chests empty. So instead I put <math>6</math> gold coins in each treasure chest, but then I had <math>3</math> gold coins left over. How many gold coins did I have?
 
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<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 10:14, 5 February 2018

Problem 17

Solution

We can represent the amount of gold with $g$ and the amount of chests with $c$. We can use the problem to make the following equations: \[9c-18 = g\] \[6c+3 = g\]

Therefore, $6c+3 = 9c-18.$ This implies that $c = 7.$ We therefore have $g = 45.$ So, our answer is $\boxed{\textbf{(C)}\ 45}.$

See Also

2017 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 16 		Followed by
Problem 18
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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