## Missing dollar Problem

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 has 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?

See if you an work it out

## Hypertext Infinity 4:38 pm

onApril 22, 2011 Permalink |This is how I worked it out. This is just the first method.

The men originally paid $30, 10 dollars for each man. 10×3=30 dollars. After that, the manager payed them back $5. So, 5÷3= 1.66666666 dollars. But, the bellboy only returned the three men $3. 3÷3=1.00 dollars. So, a man lost 0.666 cents. Three men lost 0.666×3=1.998 which is about $2. The bellboy kept the $2. So, there is no dollar missing.

## Hypertext Infinity 4:40 pm

onApril 22, 2011 Permalink |The second method I have it that the decimals make up the missing dollar. Please comment back and correct me!

## MathematicalMagician 9:46 am

onApril 23, 2011 Permalinkno, there are no decimals involved!

## Hypertext Infinity 12:30 am

onApril 24, 2011 Permalink |Well then, I guess I have no idea!

## myriam 1:00 pm

onApril 24, 2011 Permalink |in fact the total paid isn’t 27, but 28 ! since there are 3 guests : 3+25 = 28 ! and this way 28 still can’t be divided by 3 !

but 28 + 2 = 30 so no dollars lost I guess 😉

## myriam 1:03 pm

onApril 24, 2011 Permalink |I gave a wrong answer …

## myriam 1:09 pm

onApril 24, 2011 Permalink |well I’ll try again:

the 30 $ may be written this way 25 +1 + 1+ 1 + 2 ===> 27 paid and 3 with the guests !

the 27 $ paid are 3*9 , and no dollar lost !

I hope this is the correct answer ^_^

## مانيش أنا 4:45 am

onApril 26, 2011 Permalink |no dollar lost!!

in fact the 2 dollars that the belboy kept are involved in the paid ammount:

2+25=27

an they have 3 dollars back

“Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2” this makes us think that we have to add 2 to 27 to get 30$ but it’s not the case

“the 30 $ may be written this way 25 +1 + 1+ 1 + 2 ===> 27 paid and 3 with the guests !

the 27 $ paid are 3*9 , and no dollar lost ” yes that’s it 🙂

## MathematicalMagician 6:50 pm

onApril 26, 2011 Permalink |it is correct!

🙂

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