Three students share a bread. The first eats half, the second eats half of what is left, and the third eats half of that and so on....How much does each eat?

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- Mar 30th 2009, 06:27 AMzhupolongjoeThree students and bread
Three students share a bread. The first eats half, the second eats half of what is left, and the third eats half of that and so on....How much does each eat?

- Mar 30th 2009, 09:22 AMTheEmptySet
- Mar 31st 2009, 12:22 AMmathsquest
The fractions consumed by each

1 are 1/2 , 1/16 1/128 totalling ½[1+(1/8) + (1/8)2 +…]

2 are 1/4 , 1/32, 1/256 totalling 1/4[1+(1/8) + (1/8)2 +…]

3 are 1/8, 1/64 1/512, totalling 1/8[1+(1/8) + (1/8)2 +…]

[1+(1/8) + (1/8)2 +…] = 1 / (1-1/8) = (8/7). Therefore,

1 consumes (1/2) (8/7) = 4/7

2 consumes (1/4) (8/7) = 2/7

3 consumes (1/8) (8/7) = 1/7

Note 4/7 + 2/7 + 1/7 = 1