2011 AMC 10B Problem 6

Problem 6 of 25EasierAlgebra

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?

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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.