2014 AMC 10A Problem 2

Problem 2 of 25EasierAlgebra

Roy’s cat eats

\dfrac{1}{3}

of a can of cat food every morning and

\dfrac{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?

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Solution

The cat eats

\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{7}{12}

cans of food each full day. After

10

full days, it has eaten

10\cdot\frac7{12}=\frac{35}{6}

cans, leaving

\frac16

of a can. The cat finishes that remainder during its next morning feeding. The eleventh morning, counting Monday as the first, is Thursday. Thus, C is the correct answer.

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