Three men decided to split the cost of a hotel room. The hotel manager gave them a price of $30.
The men split the bill evenly, each paying $10, and went to their room. However, the hotel manager realized that it was a Wednesday night, which meant the hotel had a special: rooms were only $25. He had overcharged them $5.
He called the bellboy, gave him five one-dollar bills and told him to return it to the men.
When the bellboy explained the situation to the men, they were so pleased at the honesty of the establishment that they promptly tipped the bellboy $2 of the $5 he had returned and each kept $1 for himself.
So each of the three men ended up paying $9 (their original $10, minus $1 back) totaling $27, plus $2 for the bellboy which makes $29.
So where is the missing dollar?
There is no missing dollar. The men paid $27 and kept $3 for themselves which adds up to $30. In the story, the bellboy’s take is totaled twice. It's already included in the $27 the men paid. $25 for the manager, $2 for the bellboy and $3 for the men = $30.
It's crumpled up and is blocking the 0.04' tick on your vernier scale.
Also, a wise man once wrote that 27-2 = 25...
There Is No Missing Dollar?
They each tipped him their share of the 2 dollar bills, keeping one for themselves. That was easier than keepng the $2, having to make change between themselves. Otherwise they would have ended up cutting 2 pennies in thirds so they could each get their $0.666666666667
Paul in PA
3 x 9 = $27 which the guys paid towards the room cost.
$27 - the $2 tip = the $25 room cost.
🙂
Loyal
Here's the running account:
Check Your Math Jim?
$1.67 + $1.67 + $1.67 + $25.00 = $30.01
It appears you have forced the bellboy to invest his own $0.01 into the fray.
Paul in PA
Check Your Math Jim?
> $1.67 + $1.67 + $1.67 + $25.00 = $30.01
The principle behind the note I attach to subdivision maps pertains:
"THE SUM OF THE PARTS OF A GIVEN LINE MAY NOT EQUAL THE TOTAL SHOWN DUE TO ROUNDING."
Check Your Math Jim?> Jim Frame
You really don't insist that the sum of the distances equals the total on your plans?
"The principle behind the note I attach to subdivision maps pertains:
"THE SUM OF THE PARTS OF A GIVEN LINE MAY NOT EQUAL THE TOTAL SHOWN DUE TO ROUNDING.""
> Here's the running account:
>
>
nerd!
Check Your Math Jim?> Jim Frame
> You really don't insist that the sum of the distances equals the total on your plans?
On the contrary, the note states that the total may *not* always equal the overall due to rounding.
This note came into being about 20 years ago when the firm I was working for at the time was subdividing a 600-acre parcel into residential lots. We were churning out maps as fast as we could to keep up with the developer's demands, but the city's map checker would stop every one of them when the lot dimension totals didn't equal the block dimensions. We actually had to meet with the map checker and the Public Works Director and explain how rounding works. After much balking, they finally agreed to allow rounding discrepancies as long as we put that note on the map. I've been using it ever since. (Though I don't do many subdivisions these days -- too boring!)
Here is the Geophysical answer:
What do you want it to be?
Located at the zero side of one. Counting the divisions will alway be one more than the unit that divides them. Like the old question, to divide a 12 foot long 2 X 12 into 12 pieces requires how many saw cuts?
jud
If the rooms were $25, each man owed $8.33. When the five dollars was returned to them they should have gotten $1.67 each. Each man gave .67 cents to the bellboy.
8.33 x 3 = 24.99
1.67 x 3 = 5.01
24.99 + 5.01 = 30.00
>
> So each of the three men ended up paying $9 (their original $10, minus $1 back) totaling $27, plus $2 for the bellboy which makes $29.
>
> So where is the missing dollar?
It's a simple mis-direction.
27 (total) MINUS 2 is the 25.
I had a boss that told me "Mathamatics don't work", then proceeded to tell the riddle.
I hit that one out of the park, but in retrospect, you should never show up your boss in front of everyone.
Check the dryer!
