This actually isn’t as much a math problem, as a logic and semantics problem. It took me a few minutes to spot the logical fallacy in this problem. I knew it was there, but it was difficult to spot nonetheless.
This is a semantic fallacy. The premise is false, which you can see when you work the equation backwards. The men DID NOT pay $9.00 each for a total of $27.00 for the room. They each essentially paid $8.333 for the room for a total of $25.00. Then add back in the tip of $2.00 they gave to the hotel owner, equaling $27.00. Then add back the refund each man got back ($1.00 per man). This brings you back to your correct beginning total of $30.00.
Wording things in misleading ways is what allows swindlers to make a living. By wording it the way they have in the problem, you actually add in the $2.00 to the owner twice, and you don’t add in the $3.00 rebate to the men at all, which leaves you short $1.00.
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