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

Answer: C

Concepts:rate fraction date and time

Difficulty rating: 1140

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.

2014 AMC 10A Problem 2

Answer: C

Difficulty rating: 1140

Solution:

Problem 2 in Other Years