# Math Brain Teaser

## Main Question or Discussion Point

Three people check into a hotel. They pay $30 to the manager and go to their room. The manager finds out that the room rate is$25 and gives $5 to the bellboy to return. On the way to the room, the bellboy reasons that$5 would be difficult to share among three people, so he pockets $2 and gives$1 to each person. Now, each person paid $10 and got back$1. So they paid $9 each, totalling$27. The bellboy has $2, totalling$29. Where is the remaining dollar?

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DaveC426913
Gold Member
So they paid $9 each, totalling$27. The bellboy has $2, totalling$29.
Hint:
"Paid" = apples
"has" = oranges
oranges can only be added to oranges

Hint:
"Paid" = apples
"has" = oranges
oranges can only be added to oranges
Count how much money each person started with and how much each person ends up with.

DaveC426913
Gold Member
Count how much money each person started with and how much each person ends up with.
You know how to read obscured text, right? Select the word "Hint:" - and everything after it....

This is actually really simple...

Explanation in white.

This is a trick, really. There are thirty dollars in total. The bellboy takes two, leaving twenty eight dollars. He then gives one to each of the three, leaving twenty five dollars that have been paid. Each person PAYS $9, totaling$27, and then the bellboy takes $2 from that, leaving$25. In total, they paid $25 to the hotel and$2 to the bellboy -- which is $27 total, hence they paid$9 each. The extra three dollars they got in return are invisible, they paid $27 total ($2 to the bell boy, $25 to the rooms,) and now have an extra$1 to pocket.

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the answer is much simpler than anyone thinks, its just a trick as far as the wording goes. there are two ways to solve this.
1. with math its quite simple. they payed 25 dollars so 25/3 = ($8.333... + 1 [the one they got back]) x 3people =$28 and the bellboy has 2 so thats 30\$

2. simple really... the bellboy has 2, the people have 3, and the manager has 25 which in total is 30

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