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

$x-\dfrac{1}{2}x-\dfrac{1}{2}=\dfrac{x}{2}-\dfrac{1}{2}$

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

$\text{Remaining eggs}=\dfrac{x}{2}-\dfrac{1}{2}-(\dfrac{x}{2}-\dfrac{1}{2})\times \dfrac{1}{2}-\dfrac{1}{2}$

$=\dfrac{x}{2}-\dfrac{1}{2}-\dfrac{x}{4}+\dfrac{1}{4}-\dfrac{1}{2}$

$=(\dfrac{x}{2}-\dfrac{x}{4})+(-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{2})$

$=(\dfrac{2x-x}{4})+(\dfrac{-2+1-2}{4})$

$=\dfrac{x}{4}-\dfrac{3}{4}$

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

$\dfrac{x}{4}-\dfrac{3}{4}=0$

$\dfrac{x}{4}=\dfrac{3}{4}$

Multiply both sides by 4.

$x=3$

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