Problem solving is a huge part of mathematics. Logic is often overlooked when focusing on solving word problem, and I feel it helps a great deal. Without logic, it is almost impossible to set up the math for some word problems.
Where did the other dollar go?
- Three men rent a hotel room. Each pays $10 for a total of $30 spent on the room. The next day the hotel owner tells the three men that they over paid for the room as it only costs $25. The three men tell the owner to give them each a dollar back and he can keep two dollars.
If you do the math, each man paid $9 a piece for the room for a total of $27. The owner kept $2 which brings the total to $29.
The question is where did the other dollar go?
Hint: Try to trace where each person's money is going.
Solution:
This is a semantic fallacy. The premise is false, which you can see when you work the equation backwards. The men do pay a total of $9.00 each (total of $27.00) for the room, but only after you add in the amount they tipped the owner. They paid $25 dollars for the room and they gave the owner $2 as a tip. ($25 + 2 = $27.00). At this point the only thing to add back in to get to the original $30.00 is the $3 the men received as a refund. ($27 + $3 = $30)
Or to simply it further:
There is a misdirect in the problem when it says that when you do the math each man paid $9 each for the room, plus $2 tip. They don't. They pay a combined price of $25.00 plus the $2 tip. The problem sets up a set of facts:
Those are the facts. Once you separate those out, you can see the misdirect in the puzzle. There isn't a dollar discrepancy as listed, all the money is accounted for.
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.
Solution:
This is a semantic fallacy. The premise is false, which you can see when you work the equation backwards. The men do pay a total of $9.00 each (total of $27.00) for the room, but only after you add in the amount they tipped the owner. They paid $25 dollars for the room and they gave the owner $2 as a tip. ($25 + 2 = $27.00). At this point the only thing to add back in to get to the original $30.00 is the $3 the men received as a refund. ($27 + $3 = $30)
Or to simply it further:
There is a misdirect in the problem when it says that when you do the math each man paid $9 each for the room, plus $2 tip. They don't. They pay a combined price of $25.00 plus the $2 tip. The problem sets up a set of facts:
- $30.00 was originally given to the hotel owner
- Correct price of the room = $25
- Each man receives $1 dollar refund = $3
- The owner receives a $2 tip
- $25 for room + $2 tip for the owner = $27
- $30 - $27 = $3 which is how much the men receive back as a refund.
Those are the facts. Once you separate those out, you can see the misdirect in the puzzle. There isn't a dollar discrepancy as listed, all the money is accounted for.
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.