first of all, we want the final mixture to be 3 gallons. as you have it, we would have more than that. secondly, we are mixing pure water with vinegar solution. so one mixture has no vinegar in it.
also, a technicality here. you have an expression with x and never said what x was. that is bad practice! a good mathematician always identifies his/her variables and try to keep the ambiguity to a minimum.
so start this way: let x be the amount (in gallons) of spring water we want to add to make up our 3 gallon mixture. and let y be the amount (in gallons) of the 50% vinegar solution we add to the said mixture.
our first equation is x + y = 3. since we want both gallon amounts to add up to 3 gallons.
now, what is the second equation? remember, we want to get 0.45 gallons (15% of 3 gallons) in the final mixture.