Applications of Linear Equations Monetary Word Problem

[dajohu]

Hi,
This is the problem:
Lorraine has $7.70 in dimes and quarters. If the number of quarters is two more than twice the number of dimes, how many of each type does she have?
I know the answer is 12 dimes and 26 quarters by figuring it in my head, but my professor requires us to show work to get credit of course and I can't come up with a working formula.
What I have so far figured is this:
25x + 20x + 20 + 10x - 10x = 770
45x = 750
x = 16.666... To me this won't work and I've been working on it for quite a while and can't really figure out what I'm doing wrong. I am using a formula that the professor went over in class, but like many other times, the problems we go over in class aren't quite like what we have for homework. I would appreciate any help anyone could offer.
Thanks

 

[Data]

Let y be the number of dimes and x be the number of quarters. Then

$$25x + 10y = 770$$

and

$$x=2y+2.$$

Now just solve~

 

[dajohu]

Thanks!

Thanks a bunch, I don't know why I couldn't figure that out, I really appreciate your help.
-dajohu