To ensure he never eats the whole cake, Bobby only decides to eat half of what's left for each serving. If 2/3 of the cake are left initially, and no one else but Bobby eats the cake, how much of the cake will Bobby have eaten by his 5th serving?

Question

Trace Frederick

Mathematics

24 December, 00:05

To ensure he never eats the whole cake, Bobby only decides to eat half of what's left for each serving. If 2/3 of the cake are left initially, and no one else but Bobby eats the cake, how much of the cake will Bobby have eaten by his 5th serving?

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Answers (1)

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Gunnar Blanchard · Answer 1

1st serving: 2/3 * 1/2 = 2/6 or 1/3

2nd serving: 1/3 * 1/2 = 1/6

3rd serving: 1/6 * 1/2 = 1/12

4th serving: 1/12 * 1/2 = 1/24

5th serving: 1/24 * 1/2 = 1/48

1/3 + 1/6 + 1/12 + 1/24 + 1/48

1/3 * 16/16 = 16/48

1/6 * 8/8 = 8/48

1/12 * 4/4 = 4/48

1/24 * 2/2 = 2/48

1/48 * 1/1 = 1/48

16/48 + 8/48 + 4/48 + 2/48 + 1/48 = 31/48

Bobby ate 31/48 of the cake in total.