Trying to learn how to do these types of problems. The last one I had for homework was wrong.

How much 12% Na_{2}SO_{4}and pure water must be mixed to produce 22.8 gallons of a mixture that is 7% sodium sulfate?

I started with: Let x = the # of gallons of 12% Na_{2}SO_{4 }

And Let y = the # of gallons of 100% water

Now I thought I do (value)(quantity).

I plugged:

(0.12)(x)+ (0.100)(w) = (0.07)(22.8)

and then I distributed -

0.12x+0.100w=1.596

Now I am not sure if that is correct. And if it is, I am stuck on what to do next?