This problem explores the applications of infinite series to the wonderful world

Question

This problem explores the applications of infinite series to the wonderful world of food and beverages.

a) Tom and Jennifer are eating a candy bar. First Tome eats half of the bar, then Jennifer eats half of what remains, then Tom eats half of what remains, then Jennifer eats half of what remains, etc. How much of the candy bar will Tom eat? How much will Jennifer eat?

b) Melanie and Ryan are drinking a can of soda. First Melanie drinks one-quarter of the can, then Ryan drinks two-thirds of what remains, then Melanie drinks one-quater of what remains, then Ryan drinks two-thrids of what remains, etc. How much will Melanie drink? How much will Ryan drink?

c) Ed, Sue and Bill share an apple pie. First Ed eats half of the pie, then Sue eats half of what remains, then Bill eats half of what remains, then Ed eats half of what remains, etc. How much of the pie will each of them eat?

Explanation / Answer

tom eats = 1/2 +1/8 +.... = (1/2)/(1-1/4)=2/3
jennifer eats = 1/4 +1/16+.. =(1/4)/(1-1/4)=1/3

b)
melanie = 1/4 + 1/16 +... =1/3

ryan = 1/2 + 1/8 +... = 2/3

c)
ed = 1/2 + 1/16+... = 4/7
sue = 1/4+ 1/32+....=2/7
bill =1/8+ 1/64+...=1/7

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