SOLUTION: A Man is going to the orchard to pick apples. He enters thru 6 gates each with a guard. The man then gathers his apples. As he leaves the orchard he gives half of his pickings p

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: A Man is going to the orchard to pick apples. He enters thru 6 gates each with a guard. The man then gathers his apples. As he leaves the orchard he gives half of his pickings p      Log On


   

Question 237479: A Man is going to the orchard to pick apples. He enters thru 6 gates each with a guard. The man then gathers his apples. As he leaves the orchard he gives half of his pickings plus 1 to guard number 1, he then gives half of his new total plus 1 to guard number 2, he then gives half of his new total plus 1 to guard number 3 and so on until he has given each of the 6 guards half plus one and the man is left with 3 apples when he leaves the orchard. How many apples total did the man collect? I think the answer is 318 but I cant figure out a formula for the question.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you can use nested parentheses

((((((a/2 -1)/2 -1)/2 -1)/2 -1)/2 -1)/2 -1) = 3

adding 1 and multiplying by 2 ___ = 8

adding 1 and multiplying by 2 ___ = 18

adding 1 and multiplying by 2 ___ = 38

adding 1 and multiplying by 2 ___ = 78

adding 1 and multiplying by 2 ___ = 158

adding 1 and multiplying by 2 ___ = 318