A mystery to mathematics.?

Question

Three traveling salesmen stop for the night at a budget hotel and ask for rooms. The clerk apologises and tells them that he has only one room. "Its on special tonight." he adds, "just $30.00" The three men look at each other and say "what the heck." "$10.00 each."

Later on, the clerk realises that he over cherged the three men. The special was for $25.00 a night. Calling the bell hop over, he hands him a five dollar note and tells him to take it back to the three men.

Now, the bell hop is a smart young lad. Three people cannot equally divide five dollars so he fishes in his jeans and takes out three, one dollar bills.

Knocking on the door of the three men, he hands each one of the a dollar. "Overcharge, sorry."

Now 10 - 1 = 9.00 per salesman. 9 x 3 = 27.00 in total, plus the 2.00 the bell hop kept = $29.00

What happened to the missing dollar?

teachbio · Accepted Answer

Nice teaser! Equations are only so useful!

Once the bellhop returned the three one-dollar bills, he had only $2 left so there is no missing $1.

Your faulty math came from this:  
10 - 1 = 9.00 per salesman. 9 x 3 = 27.00 in total

In reality, the equation should be: ($10*3) -(3*$1) = $27

Bellhop keeps $2, and budget hotel has remaining $25

bag o&#39; hot air · Answer

There is no missing dollar.  The mystery comes from misleading accounting.  If we keep track of where the money is at each step, we'll see that there is no missing money.  Using S for salesmen, C for clerk, B for bellhop,

S 30
C 0
B 0

S 0
C 30
B 0

S 0
C 25
B 5

S 3
C 25
B 2

Since the salemen started with $30 and ended up with $3, they paid a total of $27, $25 of which went to the clerk and $2 went to the bellhop.  The mysterious accounting comes in when we should subtract the $2 from $27 to get the $25 for the rooms rather than adding $2 to $27 to get $29, which doesn't play a part here.

Cheers!

navig8r · Answer

There is no missing dollar.  You need to subtract the $2 the bellhop kept from the $27 paid to get the $25 that the clerk got to keep.  In other words, $25 + $3 + $2 = $30.

reddy2hunt · Answer

You're mixing apples and oranges.  You're correct in saying the men paid $27, but it's $25 to the hotel and $2 the bell hop kept.
Of the original $30, the hotel got $25, the men got $3, and the bell hop got $2.

Candifer · Answer

$25 went to the hotel, $2 went to the bell hop, and $3 back to the three traveling salesmen.  (25+2+3=30!!!!)

ironduke8159 · Answer

No mystery.

9*3 =$27
$27 - $2 = $25 = cost of room.

There is no logical reason to think that $27 + $2 = $29 has any significance.

Anonymous · Answer

use the bodmas rule.

b : bracket
o : of
d : division
m : multiplication
a : addition
s : subtraction

crankyspanky · Answer

THATS SOME SHAKY ACCOUNTING!

A mystery to mathematics.?

8 Answers