How much pure acid should be mixed with 7 gallons of a 40% acid solution in order to get a 70% acid solution?

In this item, we are going to use the concepts of total mass balance and component mass balance. We let the amount of the pure acid be equal to x. 

Total mass balance:
   7 + x = 7 + x

Hence, the total amount of the resulting solution is 7 + x

Component mass balance,
   (1)(x) + (0.4)(7) = (0.7)(7 + x)

The value of x from the component mass balance is equal to 7.

7 gallons