To solve this problem, let's go through the given information step by step:
Let's assume that A initially had x coins.
According to the given information:
- A gave half of the coins to B and 4 more besides. So, A gave (x/2 + 4) coins to B.
- B gave half of the coins to C and 4 more besides. So, B gave ((x/2 + 4)/2 + 4) coins to C.
- C gave half of the coins to D and 4 more besides. So, C gave (((x/2 + 4)/2 + 4)/2 + 4) coins to D.
Both B and D end up with the same number of coins. So, we can set up an equation:
((x/2 + 4)/2 + 4) = (((x/2 + 4)/2 + 4)/2 + 4)
Now, let's solve this equation to find the value of x, which represents the number of coins A initially had.
((x/2 + 4)/2 + 4) = (((x/2 + 4)/2 + 4)/2 + 4)
(x/2 + 4)/2 + 4 = (((x/2 + 4)/2 + 4)/2 + 4)
(x/2 + 4)/2 + 4 - 4 = (((x/2 + 4)/2 + 4)/2 + 4) - 4
(x/2 + 4)/2 = (((x/2 + 4)/2 + 4)/2)
(x/2 + 4)/2 - 4 = (((x/2 + 4)/2 + 4)/2) - 4
(x/2 + 4)/2 - 4/2 = (((x/2 + 4)/2 + 4)/2) - 4/2
(x/2 + 4)/2 - 2 = (((x/2 + 4)/2 + 4)/2) - 2
(x/2 + 4)/2 - 2 = ((x/2 + 4)/2 + 4)/2 - 2
(x/2 + 4)/2 - 2 = (x/2 + 4)/4 + 2
(x/2 + 4)/2 - (x/2 + 4)/4 = 2 + 4
(2(x/2 + 4) - (x/2 + 4))/4 = 6
((2x/2 + 8) - (x/2 + 4))/4 = 6
((2x + 16) - (x + 8))/4 = 6
(2x + 16 - x - 8)/4 = 6
(x + 8)/4 = 6
x + 8 = 24
x = 24 - 8
x = 16
Therefore, A initially had 16 coins.
The correct answer is C) 72.