A person comes into a store and say to the shopkeeper, "I will buy half of your eggs plus half of an egg. "The transaction is made. A second person comes into the store and makes the same transaction. So does a third. The shopkeeper notices tha he now has one egg left. How many eggs did he begin with?
12 and a half
To find out how many eggs the shopkeeper initially had, let's break down the problem step by step.
1. Let's assume the shopkeeper started with X number of eggs.
2. The first person comes in and buys half of the eggs (X/2) plus half of an egg (1/2). So, after the first transaction, the shopkeeper would have (X/2) - (1/2) eggs left.
3. The second person does the same transaction, buying half of the remaining eggs ((X/2) - (1/2)) plus half of an egg (1/2). After the second transaction, the shopkeeper would have ((X/2) - (1/2)) - (1/2) eggs left.
4. The third person also makes the same transaction, resulting in (((X/2) - (1/2)) - (1/2)) - (1/2) eggs left.
5. Given that the shopkeeper has one egg left, we can set up an equation to solve for X, the initial number of eggs:
(((X/2) - (1/2)) - (1/2)) - (1/2) = 1
Let's solve the equation step by step:
(((X/2) - (1/2)) - (1/2)) - (1/2) = 1
(X/2) - (1/2) - (1/2) - (1/2) = 1
(X/2) - 1 = 1
(X/2) = 2
X = 2 * 2
X = 4
Therefore, the shopkeeper initially had 4 eggs.
Work backwards:
After every time a customer buys half of the eggs there are N eggs left.
So before the transaction, there were
2*(N + 1/2)=what was there before.
Repeat the same three times you'll get what was there at the very beginning.