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matherapist

Open Questions

Old Problem

This is an easy problem and can be found on the internet by googling "10 dollar problem"
The site at the end "puzzles" has several problems that we have encountered and some we haven't.

Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn’t know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.

Now that each of the guests have been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?

Posted 148 day ago

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Answers (4)

samzappala

From the change ($5), the customers were to receive back $1.66/ea. In stead, the bellhop kept $2, by giving back $3, or $1/ea.

The original price was to be 25/3=$8.33/ea. So $8.33+$1.66=$10.

Since the bellhop kept $2, each guy lost $.66. Since $25 became the new price, the extra $1 is part of it (24+1=$25; see above). So 24/3=8; change is 3/3=1; 8+1=$9ea.
$24 part of original price.
3 change
1 part of the new price (24+1=25).
2 bellhop
-----
$30

Posted 103 day ago

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In accounting, this is mixing debits and credits. The hotel cashier receives $30.00, then withdraws $5.00 from the cash box., leaving $25.00 in the box. The hotel guests receive 1 dollar each, so their total payment was $27.00, which $25.00 is in hotels cash box and $2.00 in bellhop's pocket. There is no missing dollar.

Posted 147 day ago

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matherapist

Your answer was fine. It's a problem that uses a bit of mis direction. If you can't find the website with the problems, I'll put it in an answer but you will have to reformat it as this thread does not allow references to other websites.

Posted 147 day ago

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math_fanatic

It took me a few minutes before I got this one.
This is a trick question.

Let's start with the cash register. Forget the bellhop.
Let's say the cashier is the thief.

He sees the total should have been $25 but he
can't divide the refund 3 ways so he pulls out
$3 and gives $1 to each guest.

The amount in the register is now $27.
The cashier pockets the remaining $2 and the amount in
the register is now $25 which is exactly what should
be in there. Every dollar is accounted for.

The amount paid was $25 not $30 so we should have subtracted the guests'
$3 from $30 to get $27 and the bellhop's $2 from the $27 to get $25 instead of adding it to $27 to try to
come up with $30.

I don't know if I'm being clear so I'll try to put this another way:
After the $5 is removed from the register, the register has $25, the guests have $3, and the bellhop
has $2. 25 + 3 + 2 = 30

If there is a more eloquent way to express this let me know.

Posted 148 day ago

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