Help with Queston??? I can't figure it out!!!?

Question

Here is the question...

Albert spent all his money in five stores. In each store, he spent $1 moure than half of what he had when he entered the store. How much money did Albert have when he entered the first store?

Please explain.

Answer 1

Work backwards...

Fifth store he spent $1 more than half of his money. In order to spend all his money he would have to spend $1 plus another $1 (the other half).
x = (ending amount + 1) * 2
x = (0 + 1) * 2
x = 2
So he entered the 5th store with $2

Fourth store he spent $1 more than half of his money.
x = (ending amount + 1) * 2
x = (2 + 1) * 2
x = 6
So he entered the 4th store with $6

Third store he spent $1 more than half of his money.
x = (ending amount + 1) * 2
x = (6 + 1) * 2
x = 14
So he entered the 3rd store with $14

Second store he spent $1 more than half of his money.
x = (ending amount + 1) * 2
x = (14 + 1) * 2
x = 30
So he entered the 2nd store with $30

First store he spent $1 more than half of his money.
x = (ending amount + 1) * 2
x = (30 + 1) * 2
x = 62
So he entered the 1st store with $62

Double-checking:
He started with $62 and spent $32
2nd store he started with $30 and spent $16
3rd store he started with $14 and spent $8
4th store he started with $6 and spent $4
5th store he started with $2 and spend $2

Thus he spent all of his original $62 at the 5 stores.

Edit:
$47 is the *wrong* answer. If you spend $1 more than half, that would mean you would spend $24.50 ($23.50 is the half, then $1 more than that is $24.50). That's why $62 is correct. You spend $31 (half) plus an additional dollar for $32.
$47 *would* be the correct answer if it said, you spend $1 and then half of what remains. But that wasn't the question.

Answer 2

$47

Check it:
1st store: 47-1=46, 46/2=$23 --> spent $24, left w/ $23
2nd store: 23-1=22, 22/2=$11 --> spent $12, left w/ $11
3rd store: 11-1=10, 10/2=$5 --> spent $, 6left w/ $5
4th store: 5-1=4, 4/2=$2 --> spent $3, left w/ $2
5th store: 2-1=1 --> spent $2, left w/ $0

$1 more than (2/1) is $2.

Thus, Albert entered the 5th store with $47.

And why is everyone else adding two after they double the figure when they're working backwards? Albert spent $1 more than half. If you add $2, you get $62, but if you do it the right way, you get $47.
You should always have spent $1 more in the last store than you enter the next store with!

Answer 3

Well, you have two different answers. I'll do it my way, and see who's right. (My answer, below, is $62, worked out with algebra.)

In general, when he entered a store with y dollars, he left with y - (y/2 + 1) = y/2 - 1 = x dollars.

But that means, if he left a store with x dollars, he entered with

y/2 = x + 1 ==> y = 2x + 2 dollars. (Eq 1)

The rest is easy. We just work backward using Equation 1.

Store 5. Left with zero dollars, entered with y = 2*0 + 2 = $2
Store 4. Left with $2, entered with y = 2*2 + 2 = $6
Store 3. Left with $6, entered with y = 2*6 + 2 = $14
Store 2. Left with $14, entered with y = 2*14 + 2 = $30
Store 1. Left with $30, entered with y = 2*30 + 2 = $62

So the right answer is $62. Did anybody get that?

And here's the check:

First store. Went in with $62, spent 31+1 = $32, left with $30.
Second store. Went in with $30, spent 15+1 = $16, left with $14.
Third store. Went in with $14, spent 7+1 = $8, left with $6.
Fourth store. Went in with $6, spent 3+1 = 4, left with $2.
Fifth store. Went in with $2, spent 1+1 = $2, left with $0.

There ya go!!!