# Lost Wages in Vegas

RAY: You could write an algebraic expression to answer this puzzler. For example, if you let X represent the amount of money that he started with, then after the first day he is left with X minus one, that quantity over two minus one. OK?

TOM: Yeah.

RAY: And then that just tells you how much money he's left with. Then you can run an expression, how much he has after the second day. And the third day, and set that expression equal to zero and solve.

TOM: Yeah.

RAY: Or you could think about it backwards. If you wound up with zero then the last day he entered the casino he had to have walked in with three dollars in his pocket. So if on day three he had three dollars, then he had to have started the day before with nine dollars.

And if you work backwards to the first day, he started with 21 bucks, and that's the answer. He had 21-dollars, paid a dollar to get in, he had 20 left, lost half of it. And so on. Do we have a winner?

TOM: The winner is Roger Woods from Baton Rouge, Louisiana, and for having his answer selected at random from the pile of correct answers that we got, Roger is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com, with which he can get himself a very nice looking Car Talk baseball shirt, which is red, black, white and gray, with three-quarter-length sleeves in case you have to wipe your nose out in right field. And the scripted words, Car Talk Plaza, Our Fair City, right across the front. Congratulations, Roger!

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