An egg merchant has sold out almost all the eggs he had . a few eggs w...
Problem:
An egg merchant has sold out almost all the eggs he had. A few eggs were left with him to sell to finish the stock. He gave an offer buy half of the eggs I have and take half of an egg free then three customers came to buy eggs and he left with no egg. How many eggs were there with egg merchant at the time of declaring the offer?
Solution:
Let's assume there were x eggs with the merchant at the time of declaring the offer.
Offer by the Egg Merchant:
The egg merchant gave an offer that if anyone buys half of the eggs he has, he will give half of an egg free. It means if someone buys x/2 eggs, he will give x/4 eggs free.
Three Customers:
Three customers came to buy eggs. Let's say the first customer bought a eggs, the second customer bought b eggs, and the third customer bought c eggs.
So, the total number of eggs sold by the egg merchant is:
a + b + c
Egg Merchant's Stock:
Now, we know that the egg merchant sold all the eggs he had. So, the total number of eggs sold by the egg merchant should be equal to the total number of eggs he had at the time of declaring the offer.
Therefore, we can write the following equation:
a + b + c = x - x/2 - x/4
Simplifying the above equation:
a + b + c = 3x/4
Conclusion:
Now, we need to find the value of x that satisfies the above equation. We can assume different values of x and check which value satisfies the equation.
Let's assume that there were 48 eggs with the egg merchant at the time of declaring the offer.
So, according to the offer, if someone buys 24 eggs, the egg merchant will give 12 eggs free.
So, the total number of eggs sold will be:
a + b + c = 24 + 24 + 24/2 = 60
Now, let's substitute the values in the equation:
a + b + c = 3x/4
60 = 3 x 48 / 4
60 = 36
As we can see, the equation is not satisfied. So, we need to assume another value of x and check the equation again.
By assuming different values of x, we can find that the total number of eggs with the egg merchant at the time of declaring the offer should be 96.
Therefore, the egg merchant had 96 eggs at the time of declaring the offer.