To all my fellow math lovers, today I was posed with a question by my friend Ms. K. Ms. K is a math major like myself who finds puzzling math problems very intriguing, she came across this problem when her mom called and asked her how it worked. This problem came from a grade 7 text.
So, three guys walk into a hotel (sounds like a joke right? keep reading). The receptionist at the desk charges the men $30 to stay at the hotel for the night; each man pays $10. Later the receptionist realizes that he made a mistake and should have only charged the men $25. The receptionist then gives the bellhop the extra $5 to bring back up to the men. On the way up to the room the bellhop realizes that he doesn't know how to split $5 into three equal parts for the men, he decides to give each man back $1 (for a total of $3) and keep the remaining $2 for himself as a tip. If the men originally paid $10 and got back $1 each then that means they really only paid $9 each. $9 times 3 men is only $27. The bellhop keeps $2 for himself, making a total of $29.
What happens here? Why is there a difference in the numbers? If you add up $25 + $3 + $2 = $30 but( 3 X $9) + $2 = $29. What explanations can you come up with? The only explanation I could come up with was that if you write all the dollar amounts on a number line then there are 31 numbers (including 0) and there are 30 spaces (for the cents) in between them. Therefore I think this problem has something to do with integers, but that's open for debate.
In keeping with our problem solving activities of recent classes I thought that this problem was appropriate for us to think about. If anyone else has any suggestions as to the discrepancy in the numbers feel free to comment on this post, I will gladly take any ideas you have. I hope this puzzling question is as intriguing for you as it was for me.
So, three guys walk into a hotel (sounds like a joke right? keep reading). The receptionist at the desk charges the men $30 to stay at the hotel for the night; each man pays $10. Later the receptionist realizes that he made a mistake and should have only charged the men $25. The receptionist then gives the bellhop the extra $5 to bring back up to the men. On the way up to the room the bellhop realizes that he doesn't know how to split $5 into three equal parts for the men, he decides to give each man back $1 (for a total of $3) and keep the remaining $2 for himself as a tip. If the men originally paid $10 and got back $1 each then that means they really only paid $9 each. $9 times 3 men is only $27. The bellhop keeps $2 for himself, making a total of $29.
What happens here? Why is there a difference in the numbers? If you add up $25 + $3 + $2 = $30 but( 3 X $9) + $2 = $29. What explanations can you come up with? The only explanation I could come up with was that if you write all the dollar amounts on a number line then there are 31 numbers (including 0) and there are 30 spaces (for the cents) in between them. Therefore I think this problem has something to do with integers, but that's open for debate.
In keeping with our problem solving activities of recent classes I thought that this problem was appropriate for us to think about. If anyone else has any suggestions as to the discrepancy in the numbers feel free to comment on this post, I will gladly take any ideas you have. I hope this puzzling question is as intriguing for you as it was for me.
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