An egg salesman was asked how many eggs he had sold that day. He replied, "My first customer said, 'I'll buy half of your eggs plus half of an eggs.' My second and third customers made the same order as customer number one. When I had filled all three orders I was sold out and I did not have to break a single egg all day."
How many eggs did the egg salesman start with?
1st customer: x/2 + 1/2 = (x+1)/2, leaving (x-1)/2
2nd customer: (x-1)/4 + 1/2 = (x+1)/4, leaving (x-3)/4
3rd customer: (x-3)/8 + 1/2 = (x+1)/8 leaving 0
so,
(x+1)/2 + (x+1)/4 + (x+1)/8 = x
x = 7
it's easy to check that 4+2+1 = 7
1st = e/2 + 1/2
2nd = [(e - e/2 - 1/2) / 2] + 1/2 = e/4 + 1/4
3rd = [(e - e/2 - 1/2 - e/4 - 1/4) / 2] + 1/2 = e/8 + 1/8
e = (7e / 8) + 7/8
8e = 7e + 7
Let's break down the information given step by step:
1. The first customer bought half of the eggs plus half of an egg.
2. The second customer made the same order as the first customer, buying half of the eggs plus half of an egg.
3. The third customer made the same order as the first and second customers, buying half of the eggs plus half of an egg.
By analyzing the information, we can deduce the following:
If the first customer bought half of the eggs plus half of an egg, it means they bought an odd number of eggs. Let's call this number "x" for now.
Since the second and third customers made the same order as the first customer, they also bought an odd number of eggs.
Adding up the orders from the first, second, and third customers, we have:
Customer 1: x eggs
Customer 2: x eggs
Customer 3: x eggs
Now, we know that the salesman didn't have to break a single egg, which means he sold all of his eggs without any leftovers. Therefore, the total number of eggs must be a multiple of "x".
Now, let's look at the possible values of "x" and the corresponding multiples:
- If x = 1, the total number of eggs would be 1 + 2 + 3 = 6.
- If x = 3, the total number of eggs would be 3 + 6 + 9 = 18.
- If x = 5, the total number of eggs would be 5 + 10 + 15 = 30.
- If x = 7, the total number of eggs would be 7 + 14 + 21 = 42.
- And so on.
Since the salesman sold all of his eggs without any leftovers, the total number of eggs must be a multiple of "x". Looking at the possible values of "x", we can see that the only value that fits this condition is x = 1.
Therefore, the egg salesman started with 1 egg.
To find the number of eggs the salesman started with, let's work backwards. We know that after filling three orders (from the first, second, and third customers) he sold out his stock.
Let's assume the salesman initially had x eggs.
The first customer bought half of the eggs (x/2) plus half of an egg (1/2). So, after the first customer, the salesman had x/2 eggs left.
The second customer bought the same order as the first customer, which means the salesman sold x/2 eggs again. Now the salesman had 1/2 an egg left.
The third customer also bought the same order as the first and second customers, so the salesman sold another x/2 eggs. Now he had 1/2 an egg left.
Since the salesman had 1/2 an egg left after selling out, this means that x/2 - (3 * (x/2)) = 1/2.
Let's solve this equation to find the value of x:
x/2 - 3x/2 = 1/2
-2x/2 = 1/2
-x = 1/2
x = -1/2
However, we can't have a negative number of eggs, so the solution x = -1/2 doesn't make sense in this context.
Therefore, there is no possible number of eggs that the salesman could have started with to satisfy the given conditions.