2014 AMC 10A Problems/Problem 2

Revision as of 22:53, 6 February 2014 by Mishai (talk | contribs) (Problem)

Problem

Roy's cat eats $\frac{1}{3}$ of a can of cat food every morning and $\frac{1}{4}$ of a can of cat food every evening. Before feeding his cat on Monday morning, Roy opened a box containing $6$ 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 $\dfrac13+\dfrac14=\dfrac7{12}$ of a can of cat food. Therefore, the cat food will last for $\dfrac{6}{\dfrac7{12}}=\dfrac{72}7>10$ days. Because the number of days is greater than 10, the cat will finish eating in 11 days, which is $4 \pmod 7$, so the cat will finish on $\textbf{(C)}$ Thursday.