20% of 12 gallons

.2*12= 2.4 gallons of anti freeze make the 20% solution

2.4/12=20% , antifreeze diveded by total gallons makes the 20% solution

(2.4+x)/(12+x)=.5 , the ratio of antifreeze to total gallons must be equal to .5 for 50% solution

(x+2.4)/(x+12)=.5 , you add an x amount of gallons of antifreeze , so you have to add it to both nuemerator and denominator

(x+2.4)=.5(x+12)

x+2.4=.5x+6

x-.5x=6-2.4

.5x=3.6

x=3.6/.5 = 7.2 gallons of pure antifreeze are needed to make solution of 50%