# Where is the other buck?

Asked by cheebdragon (17100) June 8th, 2008

Three guys walk into a hotel, and they’re going to split the cost of a room. The room is \$30. They each kick in \$10 and head up to their room. The manager gets wind of it and tells the clerk the room is only \$25. He hands five \$1 bills to the bell hop and tells him to go refund the guys’ money. On the way up to the room, the bell hop gets to thinking and says to himself, “No way can three guys split \$5, I’m going to help out.” He stuffs \$2 in his pocket, knocks on the door, gives each guy back a buck and heads back downstairs to the desk, glowing in the warmth of a job well done. So now each guy has paid \$9. \$9 times 3 is \$27 plus the two the bell hop stole—only \$29! Where is the other buck?

I just found this today on a website and i thought it was kinda clever, what do you think?

Observing members: 0 Composing members: 0

What the hell!?!? How does that work?

Edit: I have a feeling people are doing the same thing I am; reading this over and over again trying to figure it out.

Allie (17407)

The problem is that you are adding the \$2 the bell hop has instead of subtracting. They each paid \$9 for a room that costs \$25 (with the discount). 3 * 9 – 2 = 25.

phoenyx (7369)

\$25 divided by 3 is \$8.33 (rounded) per person. If the bell hop gives each of them back \$1 then total is \$9.33 per person x 3 is \$28.00 plus the \$2 tip equals \$30.00

The trick is \$25 is not evenly divisible into whole numbers.

sndfreQ (11712)

a HOTEL is charging only 25\$/room. now that’s a good deal. i am too sleepy to seriously think about this question right now. but i will give it a try tomorrow because it is definitely interesting.

edit – never mind, sndfreq got it. great job!

jlm11f (12350)

Ahh, I added the \$2 instead of subtracting it. It’s a cost, not a payment to them. I get it now.

Allie (17407)

Anybody who thinks that there are taxes or any cents is wrong. The way with cents is an answer but is wrong, its just the way that the person tells the sum back to you. The way they tell it back to you is just confusing, the dollar doesn’t go anywhere, it is just not obvious at first because you don’t realize the way they told it back to you is wrong.

xxporkxsodaxx (1386)

Yes Allie is right from a more methodical approach to figuring cost-\$8.33 (\$25.00 divided by 3) + \$0.66 (1/3 of the tip)= \$9.00 total cost (room + tip) per person. \$30.00 – \$27.00 (\$9.00 per person x 3 people) = \$3.00 change split three ways.

sndfreQ (11712)

My dad used to torment me with this same riddle to me when I was a young kid. I used to torment my friends with it in return. They couldn’t figure how it worked. I never told anyone how the math is being approached wrongly, and it drove them nuts! Haha. I haven’t heard this in years. Thanks, cheebdragon. Now that I’m reminded of this again I can torment some of my workmates.

AstroChuck (36975)

.999=1 thats the key to solving this problem

Lets work through it backwards shall we.

30 dollars we have to start with. Bellhop takes two of it so we’re down to 28. Each of the men is given back 1 dollar which brings us down to the cost of the room 25\$. Now as sndfreQ said 25/3=8.3333 so in reality each man only paid 8.333333333(and so on for the room) which would bring the total cost to 24.99999999(yada yada) but since .999999 equals 1 it ends up being an even 25\$. In the problem you neglect the .999999999 thats the missing dollar right there.

dont believe that .99999=1?

assume x=.9999999

10x (9.9999)
– x ( .9999)
———————-
9x (9)

x =1

Uber: =[ Why do you torture me?

Allie (17407)

my bwain farted….
:S @, @

90s_kid (2183)

or