Adairy needs 225 gallons of milk containing 6% butterfat. how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 225 gallons

Let
x> gallons of milk containing 7% butterfat 
y> gallons of milk containing 2% butterfat 

we know that
x+y=225> x=225-y> equation 1
x*0.07+y*0.02=225*0.06> multiply by 100 both sides
7x+2y=1350> erquation 2

substitute equation 1 in equation 2
7*[225-y]+2y=1350> 1575-7y+2y=1350> 5y=225> y=45 gallons
x=225-y> x=225-45> x=180 gallons

the answer is
180 gallons of milk containing 7% butterfat 
45 gallons of milk containing 2% butterfat