Question

Mr. Zerman went shopping. In the first store he spent half of his money plus an additional dollar. At the second store he spent half of his remaining money plus an additional dollar. This pattern continued until he left the fifth store with no money left. How much money did he have before he started shopping?

Answer 1

$X To start with.

1st. Store:
Bal. = X - ((X/2)+1) = X - X/2-1 = X/2-1

2nd Store:
Bal=X/2-1 - (X/2-1)/2+1 = X/2-1 - X/4+1/2-1 = X/4 - 1/2.

3rd. Store:
Bal = X/4-1/2 - (X/4-1/2)/2+1 =
X/4-1/2 - X/8+1/4)-1 = X/8 - 1 1/4 =
X/8 - 5/4.

4th Store:
X/8-5/4 - (X/8-5/4)/2+1 = X/8-5/4 -
X/16 + 5/8 - 1 = X/16 - 13/8

5th Store:
X/16-13/8 - X/32+13/16-1 = X/32-29/16=0

X/32 = 29/16
X = $58.

Answer 2

Working backwards, he ends up with 0, so:
2(0+1)=2
2(2+1)=6
2(6+1)=14
2(14+1)=30
2(30+1)=62
If you check the math, you will find that he started with $62
62/2 -1=30
30/2 -1=14
14/2 -1=6
6/2 -1=2
2/2 -1=0
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