Posted by Kimberly on .
A man has a basket of eggs. He wants to cross a toll bridge but has no money. The first toll collector says he will let the man pass if he gives him half of his eggs and half an egg. When he gets to the next toll collector he still has no money. Again the toll collector says he will let the man pass for half of his eggs and half of egg. Third tollcollector agrees to the same deal. This leaves the man with no eggs. How many eggs did the man start out with?-
Suppse n is the number of eggs the man has to begin with. At the first toll he gives away
(1/2)n + 1/2 so he has
n - ((1/2)n + 1/2) = (1/2)n - 1/2 left
At the second toll he gives away
(1/2)((1/2)n - 1/2) +1/2 = (1/4)n + 1/4 so he has
((1/2)n - 1/2) - (1/4)n + 1/4 = (1/4)n -1/4 left
Finally he gives away
(1/2)((1/4)n -1/4) + 1/2 = (1/8)n +3/8
and has none left so
(1/4)n -1/4 = (1/8)n +3/8 so
(1/8)n = 5/8 and n = 5.
Now test this
If he starts with 5 eggs and gives away half and a half egg then
5 - 2.5 -.5 = 2 eggs
Next he gives away 1 egg and a half egg so he has
2 - 1 -.5 = .5
At the third stop all he has is half an egg so that's all he can give away.
Hopefully I read your problem correctly. Since I seem to have worked your problem completely find another one similar to it in your text and work that for practice.
Thank you very much!
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