Lost Wages in Vegas

Mar 03, 2008

RAY: This is from my Lost Wages series and it was sent in by Katherine Curtis. She writes, 'A man is visiting Las Vegas, known for gambling casinos and the like, and he falls for the local hype and heads for a casino with hopes of hitting it big.
He goes into this unusual casino that charges a dollar to enter, as well as a dollar to leave. He pays his dollar, plays the slot machines, loses half his money and in disgust pays his one dollar and leaves.

'The following day he knows he'll do better. He takes the money he has left and heads out to the same casino. He pays his buck, but just like before, he again loses half his money, and pays another dollar to leave.

'On the third day he figures he'll give it one more shot but his money is dwindling fast. The same thing happens. After paying his one dollar entrance, he loses half his money, and then pays his last dollar to get out. He's flat broke when he leaves.'

So the question very simply is, how much money did he start with?


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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