Question

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?

Tuesday

Wednesday

Thursday

Friday

Saturday

Solution:

The cat eats $\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{7}{12}$ cans of food each day. This means that it will take the cat $6 \div \dfrac{7}{12} = \dfrac{72}{7}$ days to finish all the foods. Note that this value is between $10$ and $11.$

This means that the cat will finish eating the food in $11$ days, which is $10$ days after Monday.

$10$ days after Monday is the same as $3$ days after Monday, and as such, the answer is Thursday.

Thus, C is the correct answer.

2014 AMC 10A Problem 2

Solution:

Problem 2 in Other Years