SOLUTION: Auggie spent all of his money in 5 stores. In each store, he spent $1 more than one-half of what he had when he went in. How many dollars did Auggie have when he entered the first

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Question 136627: Auggie spent all of his money in 5 stores. In each store, he spent $1 more than one-half of what he had when he went in. How many dollars did Auggie have when he entered the first store?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
He starts with x dollars, so in the first store he spends x%2F2%2B1. So when he leaves the first store he has x-%28x%2F2%2B1%29=x%2F2-1=x%2F2-2%2F2=%28x-2%29%2F2.

So in the second store he spends %28%28x-2%29%2F%282%2A2%29%29%2B1 so he has %28%28x-2%29%2F%282%2A2%29%29-1=%28x-2-4%29%2F4=%28x-6%29%2F4 left.

And so on.

I'll leave it to you to verify that when he leaves the 5th store he has %28x-62%29%2F64 dollars remaining, and by the conditions of the problem this expression must be equal to zero (because he spent all of his money). If %28x-62%29%2F64=0, then x-62=0 => x=62

Check:
Start: 62
Half of 62 is 31 plus 1 is 32, leaving 30
Half of 30 is 15 plus 1 is 16, leaving 14
Half of 14 is 7 plus 1 is 8, leaving 6
Half of 6 is 3 plus 1 is 4, leaving 2
Half of 2 is 1 plus 1 is 2, leaving 0