+128407 Homer is giving some cookies to each of his three brothers. To the oldest, he gives half of the cookies and half a cookie. He then gives half of what is now left and half a cookie to his second brother. Finally, he gives half of what is now left and half a cookie to his second brother. At no time is a cookie broken or cut. How many cookies did Homer have to begin with?
Let the total number of cookies = T
He gives the oldest T/2 + 1/2
What is left after this is T - (T/2 + 1/2) = (T/2) - 1/2
He gives the next brother (1/2) ( T/2 -1 /2) + 1/2 = T/4 + 1/4
What is left is [ T/2 - 1/2 ] - [ T/4 + 1/4 ] = T/4 - (3/4)
He gives the last brother (1/2) [ T/4 - (3/4)] + 1/2 = T/8 + 1/8
Now the sum of what he gives to each brother must be the total number of cookies
So....we have this equation
T/2 + 1/2 + T/4 + 1/4 + T/8 + 1/8 = T simplify
(7/8) T + (7/8) = T
(7/8) = T(1 - 7/8)
7/8 = T/8
7 = T = the number he statred with
Proof
He gives the oldest (1/2) 7 + 1/2 = 4
3 are left
He gives the next (1/2) 3 + 1/2 = 2
1 is left
He gives the last brother (1/2) 1 + 1/2 = 1
