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?

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
☺☺☺☺

Answer 3

To solve this problem, we need to work backwards. Let's consider the situation when Mr. Zerman left the fifth store with no money.

At the fifth store, he spent half of his remaining money plus an additional dollar. We can represent this as:

Money spent at the fifth store = (Money remaining at the fifth store) / 2 + 1

Since we know he left the fifth store with no money remaining, we can set up the equation:

0 = (Money remaining at the fifth store) / 2 + 1

By solving this equation, we find that the money remaining at the fifth store is -2. This means that he had $2 left before entering the fifth store.

To determine the money remaining at the fourth store, we reverse the process. So at the fourth store, he spent half of his remaining money plus an additional dollar:

Money spent at the fourth store = (Money remaining at the fourth store) / 2 + 1

We know that the money remaining at the fourth store was $2, so we can set up the equation:

$2 = ($2 remaining at the fourth store) / 2 + 1

Simplifying this equation, we find that the money remaining at the fourth store is $3.

We can continue this backward process for each store until we find the initial amount of money Mr. Zerman had before he started shopping.

So at the third store, he had $3 remaining, at the second store he had $5 remaining, and at the first store, he had $9 remaining.

Therefore, Mr. Zerman had $9 before he started shopping.