Difference between revisions of "2014 AMC 10A Problems/Problem 2"
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<math> \textbf{(A)}\ \text{Tuesday}\qquad\textbf{(B)}\ \text{Wednesday}\qquad\textbf{(C)}\ \text{Thursday}\qquad\textbf{(D)}}\ \text{Friday}\qquad\textbf{(E)}\ \text{Saturday}</math> | <math> \textbf{(A)}\ \text{Tuesday}\qquad\textbf{(B)}\ \text{Wednesday}\qquad\textbf{(C)}\ \text{Thursday}\qquad\textbf{(D)}}\ \text{Friday}\qquad\textbf{(E)}\ \text{Saturday}</math> | ||
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| + | == Solution == | ||
| + | Each day, the cat eats <math>\dfrac13+\dfrac14=\dfrac7{12}</math> of a can of cat food. Therefore, the cat food will last for <math>\dfrac{6}{\dfrac7{12}}=\dfrac{72}7>10</math> days. | ||
| + | Because the number of days is greater than 10, the cat will finish eating in 11 days, which is <math>4 \pmod 7</math>, so the cat will finish on <math>\textbf{(C)}</math> Thursday. | ||
Revision as of 21:53, 6 February 2014
Problem
Roy's cat eats 
of a can of cat food every morning and 
of a can of cat food every evening. Before feeding his cat on Monday morning, Roy opened a box containing 
cans of cat food. On what day of the week did the cat finish eating all the cat food in the box?
$\textbf{(A)}\ \text{Tuesday}\qquad\textbf{(B)}\ \text{Wednesday}\qquad\textbf{(C)}\ \text{Thursday}\qquad\textbf{(D)}}\ \text{Friday}\qquad\textbf{(E)}\ \text{Saturday}$ (Error compiling LaTeX. Unknown error_msg)
Solution
Each day, the cat eats 
of a can of cat food. Therefore, the cat food will last for 
days.
Because the number of days is greater than 10, the cat will finish eating in 11 days, which is 
, so the cat will finish on 
Thursday.
