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Puzzle Details

Last week I received a cheque from my Grandma and I cashed it at the BrainBashers bank.

I had spent £5.02 before I realised the bank had made a mistake.

They had swapped the pounds with the pence.

I now had exactly 3 times the value of the original cheque.

What was the original cheque's value?

[Ref: ZYEK] © Kevin Stone

We are told that:

(swapped amount - 5.02) = 3 x original amount

If we call the original amount x.yy, and convert to pence to give 100x + y. The swapped amount is therefore 100y + x. Giving:

(100y + x) - 502 = 3 x (100x + y)

100y + x - 502 = 300x + 3y

97y - 502 = 299x

y = 299x + 502
----------
97

This is an equation that can be solved in a number of ways, the easiest being trial and error.

Since both x and y have to be whole numbers, we quickly find that x=10 gives y=36.

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