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musicgold

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## Homework Statement

I am trying to solve the following puzzle. The problem is that there are two unknowns and I could come up with only one equation.

A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel ( 5 cents) on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?

## Homework Equations

Let x - number of dollars and y - number of cents

check amount - ## 100x + y ##

paid amount - ##100y + x ##

amount left after spending a nickel - ## 100y + x - 5 ##

So the first equation we get is:

## 100y + x - 5 = 2 (100x + y) ##

After solving it, we get

## y = \frac { 199x + 5 } { 98} ##

## The Attempt at a Solution

As there is not enough info for another equation, I tried the trial and error approach. To get a whole number the numerator has to be a multiple of 98. To have an even number in the numerator, x has to be an odd number.

I tried using a few values of x but didn't get an answer. I am not sure if I am headed in the right direction. Is there a better way of doing this?

Thanks.