Question 16261
Here's one approach:  the 30 gallons of 70% antifreeze solution is 30% water and you want to make a solution that is 60% antifreeze and 40% water. So you will add x gallons of water to the 30% water solution.
Change the percents to their decimal equivalents.  

{{{30(0.3) + x = (30 + x)(0.4)}}} Simplify and solve for x, the number of gallons of water to be added.
{{{9 + x = 12 + 0.4x}}} Subtract 0.4x from both sides.
{{{9 + 0.6x = 12}}} Subtract 9 from both sides.
{{{0.6x = 3}}} Finally, divide both sides by 0.6
{{{x = 5}}}

You will need to add 5 gallons of water to the 30 gallons of 70% antifreeze solution to make 35 gallons of 60% antifreeze solution.

Check:

{{{30(0.3)+ 5 = 35(0.4)}}}
{{{9 + 5 = 14}}}