Take a shot at this math problem

[xXxAuroraxXx]

3 Guys walk into a hotel

The person at the counter says it's 30$ for a room for all 3 of them

The 3 guys pay 10$ each to split up the cost evenly

Later on the night the manager knocks on there door and says he made a mistake and it was only 25$ for the room. He gives them back 5$

Each of the guys take 1$ and give the remaining 2$ to the bell boy.

 

So, each person payed 9$ total 9*3 = 27$ + the 2$ for the bell boy = 29$

 

What happened to the remaining dollar?

[Dave]

It's not really a math question - it's more of a trick question. The total cost for each of the men is $9 => $27 total price, yes. But that includes a $2 tip from their original money - there is no missing dollar.

[xXxAuroraxXx]

I don't understand your answer... please explain it a little more.

 

I asked this to my math teacher last year and she said it was an insolvable math problem.

[Dave]

Erm, it's certainly not unsolvable.

 

Think about this a little; at the beginning of the problem, the men give $30 to the hotel. At the end of the problem, they've given $2 to the bellboy, and they've each paid $9 ($27 in total).

 

The question says:

 

So, each person payed 9$ total 9*3 = 27$ + the 2$ for the bell boy = 29$

 

This isn't the calculation you should be doing - infact, it's pretty meaningless. The men paid $27 total, and the bellboy pocketed $2 from that $27, which means the men paid $25 (the price of the room) plus the tip ($2).

 

This is a pretty old problem tbh. I've tried to explain it by taking the wording a little bit from here, that has a couple other approaches that might enable you to get to grips with it a bit more.

[xXxAuroraxXx]

whoaaa wait.

 

The 2$ was in their change....not the original amount they paid.

[NSX]

dave, I was looking through the site you put up, how would you explain this:

 

There are actually no negative numbers

Did you know there are actually no negative numbers? Think about it, have you ever actually seen a negative number of geese? Ever wonder why?

 

It's not what you think! The reason there are no negative numbers is simply that -1 is just another way of writing 1. Watch, I can prove it. I'll even explain it as I go along.

 

Certainly, you'll have to allow me to start with

-1 = -1

Then, if I divide both sides by 1, I get

-1/1 = -1/1

Now, we know that -x/y = -(x/y) = (-x)/(y) = (x)/(-y). It doesn't matter where you put the minus sign. So, from that we get

-1/1 = 1/-1

And, if we take the square root of both sides, we get

root(-1/1) = root(1/-1)

But we can split the square roots out, so

root(-1) / root(1) = root(1) / root(-1)

Now, we can cross multiply (to get rid of the fractions), and get

root(-1) * root(-1) = root(1) * root(1)

But surely root(x) * root(x) = x. That's the definition of root(x), so

-1 = root(-1) * root(-1) = root(1) * root(1) = 1

Which leaves us with

-1 = 1

Which is what I told you originally. So you can see that there really are no negative numbers.

 

If you don't agree, try examining the proof closely. You can see I supported each step along the way.

 

for me, it's the part with -x/y = -(x/y) = (-x)/(y) = (x)/(-y)

[Dave]

Okay, let's look at it another way.

 

Look at the total amounts spent and received.

 

The hotel received $30 and paid a $5 refund; totals $25 gain.

The men spent $30, received a $5 refund then paid $2 to the bellboy; totals $27 deficit - this includes the $2 spent paying the bellboy, so the men actually spent $25 on the room, and $2 tipping the bellboy.

[ph1sher]

end situation:

manager has 25

guys have 3

bellboy has 2

total of 30

 

the 27+2 calculation is erroneous since you are adding the tip twice. it should be that the men spent 27 (25 to the manager and 2 to the bellboy) but are now holding onto 3.

[Dave]

for me, it's the part with [b']-x/y = -(x/y) = (-x)/(y) = (x)/(-y)[/b]

 

I think either that, or the fact he's taking square roots of negative numbers and odd things can happen.

[ph1sher]

dave' date=' I was looking through the site you put up, how would you explain this:

 

 

 

for me, it's the part with [b']-x/y = -(x/y) = (-x)/(y) = (x)/(-y)[/b]

 

i think the proof is invalid because root(x/y)=(root x)/(root y) only works where x and y are both positive. The principle does not hold, and thus invalidates this proof, when there are negative numbers.

[NSX]

When the 5 dollar discount was given, it meant that the bill came to $25, making each person pay (25/3) = $8.33. The manager took 2 bucks and gave back 3, meaning the bill came to $28 (25 + 3), making each person pay (28/3) = $9.33. Therefore, (9.33*3) + 2 = 30.

[mossoi]

That's not quite right.

 

The manager took 2 bucks and gave back 3 which means that the bill came to $27 (25 + 2) not $28. Each man paid $9 (27/3) to cover both the room and the tip.

 

The answer to this incarnation of this problem is in the error here:

 

"So, each person payed 9$ total 9*3 = 27$ + the 2$ for the bell boy = 29$"

------------------------------------------------^

 

It should read:

 

Each person paid $9 (total 9*3 = $27) to cover the room and the tip and was refunded $1 (total 1*3 = $3). 27 + 3 = $30

 

The discrepancy comes from the original problem including the bellboy's tip twice.

[Sayonara]

We've already done this one twice.

 

Because it's so damned old

[Dave]

Aye, it's true.

[xXxAuroraxXx]

Heh, good job Dave. The money is all there. There isn't a missing dollar, it's just a matter of how you word it.

[Dave]

Yeah. You really have to watch the wording of the question; one slight little misphrase and it throws you off very easily (as shown quite nicely in this question).