lvan Posts: 1, Reputation: 1 New Member #1 Jan 15, 2009, 09:41 PM
Finding an equation
I have a story problem that I cannot figure out. If someone could point me in the right direction I would love it.

Mary had a basket of hard-boiled eggs to sell. She sold half her eggs plus half an egg. Next she sold half her eggs and half an egg. The same thing occurred on her third, fourth and fifth times. When she finished, she had no eggs in her basket. How many did she have when she started?

I was trying things like 5(1/2x-1/2) = 0 thinking that x was the total eggs. Then I tried 5(x/.5-.5)=0 I think I am on the wrong track completely. Nothing works. Help! I'm very frustrated. :confused:
 galactus Posts: 2,271, Reputation: 282 Ultra Member #2 Jan 16, 2009, 12:20 PM
This is a recurrence relation.

$s_{n}=\frac{1}{2}s_{n-1}-\frac{1}{2}$

If we solve this relation, we get $s_{n}=32(\frac{1}{2})^{n}-1$

Now, we can find the number of eggs for any value of n between 0 and 5 just by plugging in the n value.

Plug in n=0 and see what you get. That is the number at the beginning.
 Credendovidis Posts: 1,593, Reputation: 66 - #3 Jan 16, 2009, 08:16 PM
Each step : Sn=Sn-½Sn-1/2 --> Sn=(½Sn-½)
There are 5 steps --> Sn=(½Sn-½)5
After 5 steps Sn=0

Step5=½Sn-½=0 ---> Sn=1
Step4=½Sn-½=1 ---> Sn=3
Step3=½Sn-½=3 ---> Sn=7
Step2=½Sn-½=7 ---> Sn=15
Step1=½Sn-½=15 --> Sn=31

:)

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