2023 AMC 8 Problem 10

Question

Harold made a plum pie to take on a picnic. He was able to eat only

\frac{1}{4}

of the pie, and he left the rest for his friends. A moose came by and ate

\frac{1}{3}

of what Harold left behind. After that, a porcupine ate

\frac{1}{3}

of what the moose left behind. How much of the original pie still remained after the porcupine left?

\dfrac{1}{12}

\dfrac{1}{6}

\dfrac{1}{4}

\dfrac{1}{3}

\dfrac{5}{12}

Concepts:fraction

Work with the fraction of the original pie remaining

After Harold,

\frac34

remains; after the moose, multiply by

\frac23

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Harold left

1 - \frac{1}{4} = \frac{3}{4}

of the pie for his friends.

The moose ate

\frac{1}{3} \cdot \frac{3}{4} = \frac{1}{4}

of the pie, leaving

\frac{3}{4} - \frac{1}{4} = \frac{1}{2}

of the pie.

Finally, the porcupine ate

\frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6}

of the pie. This leaves

\frac{1}{2} - \frac{1}{6} = \frac{1}{3}

of the pie.

Thus, D is the correct answer.

Problem 10 in other years