SOLUTION: Amanda leaves with a basket of hard-boiled eggs to sell. At her first stop she sold half her eggs plus half an egg. At her second stop she sold half her eggs plus half an egg. T

Question 497525: Amanda leaves with a basket of hard-boiled eggs to sell. At her first stop she sold half her eggs plus half an egg. At her second stop she sold half her eggs plus half an egg. The same thing occurs at her third, fourth, and fifth stops. When she finishes, she has no eggs in her basket. How many eggs did she start with. Answer is 31. What is the formula to figure out how many eggs?
Found 2 solutions by josmiceli, htmentor:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the number of eggs she starts with
After 1st stop, she has

After 2nd stop, she has

After 3rd stop, she has

After 4th stop, she has

After 5th stop, she has

It is given that , the number of eggs
she ends up with is zero, so

So, after the 4th stop,

After the 3rd stop,

After the 2nd stop,

After the 1st stop,

She started with 31 eggs
check answer:
31 - ( 15.5 + .5 ) = 31 - 16
31 - 16 = 15
------------
15 - ( 7.5 + .5 ) = 15 - 8
15 - 8 = 7
---------
7 - (3.5 + .5) = 7 - 4
7 - 4 = 3
----------
3 - (1.5 + .5) = 3 - 2
3 - 2 = 1
---------
1 - (.5 + .5) = 1 - 1
1 - 1 = 0
---------
OK
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Amanda leaves with a basket of hard-boiled eggs to sell. At her first stop she sold half her eggs plus half an egg. At her second stop she sold half her eggs plus half an egg. The same thing occurs at her third, fourth, and fifth stops. When she finishes, she has no eggs in her basket. How many eggs did she start with. Answer is 31. What is the formula to figure out how many eggs?
===============================================================================
Let N = the number of eggs she starts with
The number of eggs sold at the 1st stop =
Therefore the number of eggs remaining after the 1st stop =
The number sold at the 2nd stop =
And the number remaining after the 2nd stop =
The number of eggs remaining after the n-th stop =
Since no eggs remain after the 5th stop, we can write

This equation is satisfied if N=31
Ans: 31 eggs
Check (eggs sold):
1: 31/2 + 1/2 = 16
2: 15/2 + 1/2 = 8
3: 7/2 + 1/2 = 4
4: 3/2 + 1/2 = 2
5: 1/2 + 1/2 = 1
Total = 31
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