A verbal math problem.

[RoyY51]

I heard this many years ago, on the Mark and Brian radio show (KLOS).

3 guys check into a motel: the desk clerk says; "That will be $30", so each guy hands the clerk $10 and off they go. A few seconds later, the manager comes down and asks: "Did you remember that we have that $25 special going on?" When the clerk says he didn't, the manager responds: "Here's 5 one-dollar bills...run up and give this to them." On the way up, the clerk thinks: "These guys don't know I owe them money...or how much. If I gave them $3, they'd be happy...and I could pocket $2."...and so he does. When he gets to the room, he says: "Guys, I made a slight mistake...you each get back a buck!" He then hands each man a dollar.

So...

Each man paid $10, each man got back $1, so each man paid $9.

3x9=$27

The two dollars in the clerk's pocket makes $29.

Where's the last dollar?

[markw]

I heard this many years ago, on the Mark and Brian radio show (KLOS).

3 guys check into a motel: the desk clerk says; "That will be $30", so each guy hands the clerk $10 and off they go. A few seconds later, the manager comes down and asks: "Did you remember that we have that $25 special going on?" When the clerk says he didn't, the manager responds: "Here's 5 one-dollar bills...run up and give this to them." On the way up, the clerk thinks: "These guys don't know I owe them money...or how much. If I gave them $3, they'd be happy...and I could pocket $2."...and so he does. When he gets to the room, he says: "Guys, I made a slight mistake...you each get back a buck!" He then hands each man a dollar.

So....So far, so good, but now it all goes to hell


Each man paid $10, each man got back $1, so each man paid $9.

3x9=$27Technically true, but that's not the way the math works.


The two dollars in the clerk's pocket makes $29.

Where's the last dollar?Simply stated, the bellboy kept dollars 26 and 27 and gave the three men dollars 28, 29 and 30.

How is that you say? Let's look at this another way.

Each man paid $10 for a total of $30. That we can all agree on.

Now, the bellboy gives gave man # 1 a dollar, Now they paid $29.

He now gives man # 2 another dollar, Now they paid $28.

He finally gives man # 3 the third dollar, Now they paid $27.

Dollar 26 and 25 are in the bellboys pocket.

It's all in how the math is done and how the problem is stated.

[RoyY51]

I agree...it's all in how you do the math. There are always several ways to get the answer to a math problem but the answer is always supposed to be the same.

So, why doesn't this way work?

[markw]

I agree...it's all in how you do the math. There are always several ways to get the answer to a math problem but the answer is always supposed to be the same.

So, why doesn't this way work?Re-read the subject line of my first post. Then re-read my post.

If those don't answer your question, there's not much more I can say. Ask the person who laid this on you to explain it better.

[RoyY51]

Your post explains why your way works. It does not explain why my way doesn't.

[markw]

Your post explains why your way works. It does not explain why my way doesn't.I did. Two ways.

I can explain it to you, and I did, twice, but I can't understand it for you.

Here'a one last try.

They paid $30 for the room.

They got 3$ change, so they paid $27.

The bellboy got a $2 tip, but they don't know it.

That $3 change and the $2 tip equals that $5. It's all there.

I'm done here.

[RoyY51]

I did. Two ways.

I can explain it to you, and I did, twice, but I can't understand it for you.

I'm done here.

No, you didn't...twice. You merely offered another way to get the correct answer. As I previously stated, there are always alternate ways to solve a math problem.

But my original question remains.

[markw]

No, you didn't...twice. You merely offered another way to get the correct answer. As I previously stated, there are always alternate ways to solve a math problem.

My original question remains.So answer it smart guy. ..or you shooting blanks.

[RoyY51]

So answer it smart guy. ..or you shooting blanks.

Now,now...lets not be so hasty. Let's let some of the other denizens of the Audio Jungle chime in first...

[markw]

Now,now...lets not be so hasty. Let's let some of the other denizens of the Audio Jungle chime in first...You asked where the other dollar was. I told you. ..and showed you several times

It's pretty lame when one cannot admit when their puzzle was solved..

[JohnMichael]

If it is a verbal math problem why do I have to read it?

[RoyY51]

You asked where the other dollar was. I told you. ..and showed you several times

It's pretty lame when one cannot admit when their puzzle was solved..

markw:

Of course you're right...and I will be sending greenies your way. You have demonstrated two ways to get the correct answer, and there is at least one more that I know of. It is, after all, just simple addition and subtraction. But the point of this exercise was not to solve the puzzle by alternate methods, but to figure out why the originally stated method does NOT work. That's the hard part. In all the years that I've been presenting this conundrum, no one (including a Harvard Math Professor) has been able to explain it, at least not to MY satisfaction. They have all, like you, presented me with alternative methodologies but never addressed the real question: why doesn't the original scenario work?

It could very well be that, as you have ventured, I'm incapable of comprehending the answer. Given the fact that I'm old, and math was never my strong suit, it's a definite possibility.

Sorry to get you riled...it was never my intention to provoke flames. I was just trying to get some other posters and viewpoints involved...and hoping for a "lightbulb moment".

[markw]

As all my examples have demonstrated, the only way for the numbers to work is to count DOWN from 30, not up to it.

Yes, 9 x 3 equals 27. So does 30 - 3. The statement "The two dollars in the clerk's pocket makes $29." has no bearing on the math involved and it's insertion here is purely to mislead the reader, and perhaps yourself, towards counting UP from that 27 instead of down. One might even call it an outright lie.
.
ergo, my original subject "misdirection".

[StevenSurprenant]

The confusion is that you add the $2 that the clerk kept, but it should be subtracted from the total that the men spent ($27)... The cash drawer has $25 in it and the clerk has $2 in his pocket. This equals the total that the men spent ($27)

Made me think... good one!

[GMichael]

Once the $5 was given to the clerk, the new cost of the room is $25. That's what it should add up to. Not $30. $30 is no longer a constant pertinent to the situation.

$9 x 3 = $27
$27 - $2 = $25

It works out fine as long as you understand that $30 is not the goal. $25 is.