How many gallons of a 70 percent antifreeze solution must be mixed with 70 gallons of 25 percent antifreeze to get a mixture that is 60 percent antifreeze?

Suppose G gallons are required. At 70% concentration, this will contain 0.7*G gallons of antifreeze.

The 70 gallons of 25% contains 17.5 gallons of the active ingredient.

In total, then, there are (G + 70) gallons containing 0.7G + 17.5 gallons of antifreeze and this represents 60%.

So (0.7G + 17.5) / (G + 70) = 60/100

10*(0.7G + 17.5) = 6*(G + 70)

7G + 175 = 6G + 420

G = 420 - 175 = 245.

Answer: 245 gallons.