x = gallons of the 50% solution
y = gallons of the 75% solution
The total volume of the new mixture is 50 gal, so
x + y = 50
Each gal of 50% solution contributes 0.5 gal of acid, and each gal of the 75% solution contributes 0.75 gal of acid. The final mixture needs to have a concentration of 60% acid, which amounts to 0.6*(50 gal) = 30 gal of acid, so
0.5x + 0.75y = 30
Solve for x and y :
y = 50 - x
0.5x + 0.75(50 - x) = 30
0.5x + 37.5 - 0.75x = 30
7.5 = 0.25x
x = 30 ==> y = 20
