Question 265884
let x gallons of 30% alcohol solution be taken

it contains 0.3x gallons of alcohol

let y gallons of 70% alcohol solution be taken

it contains 0.7x gallons of alcohol

now to get 16 gallons 

x+y=16  ------------------ equation 1

and to have a 60% alcohol solution 

the amount of alcohol must be 60% of 16 = 9.6 gallons

so 0.3x+0.7y = 9.6 ------------- equation 2

now multiply eq.1 by 0.3 and subtract it from eq.2

we get 0.4y = 4.8

so  y=12

and x=4

So 4 gallons of 30% alcohol solution and 12 gallons of 70% alcohol solution should be mixed to get 16 gallons of 60% alcohol solution.