Question

On Halloween Casper ate $\frac{1}{3}$ of his candies and then gave $2$ candies to his brother. The next day he ate $\frac{1}{3}$ of his remaining candies and then gave $4$ candies to his sister. On the third day he ate his final $8$ candies. How many candies did Casper have at the beginning?

$30$

$39$

$48$

$57$

$66$

Solution:

Work backward. Before giving $4$ candies to his sister, Casper had $12$ candies, because he ended the second day with $8$ .

Those $12$ candies were $\dfrac23$ of what he had after the first day, so after the first day he had $18$ candies.

Before giving $2$ candies to his brother, he had $20$ candies. This was $\dfrac23$ of his original amount, so he began with $30$ candies.

Thus, A is the correct answer.

2011 AMC 10B Problem 6

Solution:

Problem 6 in Other Years