Word problem giving us a headache. Can someone help us?

I am asking for my 7th grade daughter. I hve gotten a different answer from everyone I ask. Here is the problem. Can you help? :?


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?-

Start with last collector:
in order to have -1/2 egg leave 0 eggs, there must have been 1/2 egg;
that 1/2 egg is from 1/2 of what was left: so 1 HAD to be left (after 2nd collector)

Keep going up similarly, and only 4, then 7 possible.

coll1: 7 * 1/2 = 3 1/2 + 1/2 = 4; 7 - 4 = 3

coll2: 3 * 1/2 = 1 1/2 + 1/2 = 2; 3 - 2 = 1

coll3: 1 * 1/2 = 1/2 + 1/2 = 1; 1 - 1 = 0

Geezzz...just got hungry for scrambled eggs :wink:

Thank you so much. You are the only one who has given this answer and I was actually able to understand the process. :shock: That is a great accomplishment for those of us mathematically challenged.