Bases & Congruence's decimal problem

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This is a question for a university assignment I have. I'm not after more of a "how-to".

I purchased a number of items that cost $32.70                

each and some other items that cost $115.30 each.

The total cost of my purchases was $5207.60 . How many items of each type did I purchase?

So I understand that the question is of the form:

5207.60 = 115.30Y + 32.70X

From there do i make it (using Euler's method) 115.30 = (32.70*3) +17.20 > and so on until i find the lowest common denominator, then work backwards from there?

I'm confused about what to do about the decimal. I solved it by making a computer program to try out a bunch of variables to get X = 57 Y = 29 (but that doesn't really look good on a assignment) so I am a bit stumped. Any help would be very appreciated.