Maths Puzzle

[devayaani]

Hallo all,
I am not sure if this is the right place to ask my question. If not , my apologies.
I have been trying to solve this puzzle but am frustrated at not being able to solve it.
So, thanks if you can give the answer and how to solve this mathematically by using high school algebra or maths of that level.
Here is the question:
A customer presented a cheque to the cashier in the bank. The cheque had pounds and pence. (say he has written A pounds and B pence). The cashier blundered and gave the customer B pounds and A pence (transposed the figures, that's all.) The dishonest customer has quietly pocketed the money (wrong amount) and left the bank. Now he spent £ 25 and 74 pence. After spending this much money, he is now left with a cash equal to the exact amount he had written on the cheque!
How much wsa the amount he had written on his cheque?

Thanks for the answer and also the method to solve this puzzle.
(I apologise if this is a wrong place to seek help.)
Devayaani

[jim360]

Hi -- is there any more information for this problem? Only I'm coming up with a large set of solutions rather than just the one.

[Prudie]

Assume original check was for £A.B and transposed you were given £B.A
Put this all in pence:
Original amount 100A +B
Given amount 100B + A
We know he spent 2574p and ended up with 100A+ B left over
So we can make the equation
100B + A - 2574 = 100A + B
re-arranging to get
99B - 99A = 2574
so B-A = 26
As it's real numbers we know B is greater than A and 26 more.
I then started with trial and error but the very first one works
ie if B = 99 (the maximum it could be) then A must be 73
So you got £99.73 form the bank
Spent £25.74 which leaves £73.99
So your two answers are £99.73(given) and £73.99 (original cheque)

There may be other solutions??

[bhg481]

As Jim says, we need more information for a single answer - 98 works as well in your solution Prudie.

[Prudie]

Yes bhg just trying a few more and they do work as long as 26 difference is used.

[bhg481]

We've got 2 unknowns and 1 equation - it can't have a unique solution.

[jim360]

On the other hand it's nice to see other people coming to the same conclusions and indeed setting it up in the same way.

[ToraToraTora]

2 unknowns with 2 equations bhg, classic simultaneous equation territory.

[bhg481]

1st equation B.A -A.B = 25.74

and the second equation is? TTT

[Tuvok]

Surely the maximum pence that could be transposed is 99p

[maggiebee]

Always failed maths and my attempt to solve this only reinforces my failure.

[tonyav]

It wasn't my favorite subject either, maggie ;-)

[bhg481]

Correct Tuvok, so any value of B from 26 to 99 is valid, assuming if zero pounds and 26 pence was written on the cheque the cashier was silly enough to give him £26.00.

[Prudie]

"ie if B = 99 (the maximum it could be)"
I have already said this

[bhg481]

I don't think we can improve on Prudie's answer unless the OP realises that "maximum" or "minimum" amount has been omitted from the question.

[devayaani]

Hallo,
Thanking you all for your suggestions and comments.
Now I am surprised that Prudie has given a correct but a different answer and as suggested by prudie there might be other answers (which I do not know).
But the only answer given in the book I read sometime ago (and had noted the puzzle on a paper!) is that 23 pounds and 49 pence.
Thanks to you all, once again.

By the way there is no further information provided in the puzzle apart from what I have already given.
Devayaani

[jim360]

Thanks for confirming that there's nothing else to the puzzle that you know of, which leaves us wondering what the author had in mind -- independently three of us found a whole set of solutions, and I can assure you that they're all correct based on the information given. It would be interesting to see the solution provided by the book. No idea what the book was called?

[devayaani]

jim360,
Thanks again.
I am afraid I have not made a note of the (author) puzzle book I had read several years ago.
I had simply written down the puzzle on a piece of paper when I had borrowed that book from the library.
Now sadly the library is not in existence - thanks to the internet !!!
Devayaani

[Jackdaw33]

I still can't help feeling that there is something missing to limit it to that one answer. e.g.'if the total of £ and p = 72....'

[jim360]

Ah, well, hardly your fault.

Hopefully Prudie's answer explains the method absent the extra information needed to pick a particular solution.

[Gizmonster]

I get same as everyone else:
B - A = 26
where A = amount of pounds written on original cheque and B = amount of pence written on original cheque.

.... lots of possible answers available .....