How do I solve this algebra problem/application

Here's the question:

Patricia buys a combination of 45¢ stamps and 53¢ stamps at a store. If she spends exactly $25.55 on 55 stamps, how many of each type did she buy?

I think you're supposed to set up a system of linear equations to solve it. But I'm very confused. I'll take any method. Thanks in advance for any help -- I'd really appreciate it.

x 45¢ stamps, so (55-x) 53¢ stamps

45x + 53(55-x) = 2555

8x = 53*55 - 2555 = 360

ans: 45 @ 45¢, 10 @ 55¢
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ps:
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i have used a single variable, x, rather than a system of equations for simplicity. a nice commonsense method for such q's is
let P buy all 45¢ stamps, spending 55*45 = 2475¢, 50¢ short of the target
this can be made up by substituing 10 45¢ stamps by 55¢ ones