An egg-seller sold 2 eggs more than half the number of eggs in his basket. He then sold 2 eggs fewer than half of the remaining eggs in his basket. If he was left with 28 eggs, how many eggs were in the basket at first?
108
To solve this problem, let's break it down step by step.
Let's assume that the number of eggs in the basket at first was x.
According to the problem, the egg-seller sold 2 eggs more than half the number of eggs in his basket. This can be written as:
x/2 + 2
After selling these eggs, the remaining eggs in the basket would be:
x - (x/2 + 2) = x/2 - 2
Now, the egg-seller sold 2 eggs fewer than half of the remaining eggs in his basket. This can be written as:
(x/2 - 2)/2 - 2
According to the problem, the remaining eggs in the basket after this sale were 28. So, we can equate the above expression to 28 and solve for x:
(x/2 - 2)/2 - 2 = 28
Multiplying both sides by 2, we get:
x/2 - 2 - 4 = 56
Simplifying further:
x/2 - 6 = 56
Adding 6 to both sides:
x/2 = 62
Multiplying both sides by 2:
x = 62 * 2
x = 124
Therefore, there were 124 eggs in the basket at first.