Question

A lay came to the market to sell eggs . We first customer bought 1/2 of all her eggs and 1/2 of an egg. Her second customer bought 1/2 of all the remaining eggs and 1/2 of an egg. At this point she had sold all her eggs. So how many eggs did the lady have when she came to the market

Answer 1

Given:

First customer bought 1/2 of all eggs of lady seller and 1/2 of an egg.

Her second customer bought 1/2 of all the remaining eggs and 1/2 of an egg.

At this point she had sold all her eggs.

To find:

The number of egg the lady have when she came to the market.

Solution:

Let x be the number of egg that the lady have when she came to the market.

First customer bought 1/2 of all eggs of lady seller and 1/2 of an egg. So, the number of remaining eggs after first customer is

`x-(1)/(2)x-(1)/(2)=(x)/(2)-(1)/(2)`

Her second customer bought 1/2 of all the remaining eggs and 1/2 of an egg. So, the number of remining egg after second customer is

`\text{Remaining eggs}=(x)/(2)-(1)/(2)-((x)/(2)-(1)/(2))* (1)/(2)-(1)/(2)`

`=(x)/(2)-(1)/(2)-(x)/(4)+(1)/(4)-(1)/(2)`

`=((x)/(2)-(x)/(4))+(-(1)/(2)+(1)/(4)-(1)/(2))`

`=((2x-x)/(4))+((-2+1-2)/(4))`

`=(x)/(4)-(3)/(4)`

At this point she had sold all her eggs. It means the remining eggs is 0.

`(x)/(4)-(3)/(4)=0`

`(x)/(4)=(3)/(4)`

Multiply both sides by 4.

`x=3`

Therefore, the lady came to the market is with 3 eggs.