2011 AMC 10B Problem 6

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

Work backward from the final

8

candies

Before giving away

4

, Casper had

12

, which was two thirds of the previous amount

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.

Problem 6 in other years