Achemist has one solution that is 80% acid and another solution that is 30% acid. how much of the first (80%) solution is needed to make a 400 l solution that is 62% acid?

Let x be the quantity of solution one in mixture.
so solution 2 would be (400-x) L

according to ques.
80% of x + 30% of (400-x) = 62% of 400
i.e. 80*x/100 + 30*(400-x)/100= 62*400/100
=> 80x - 30x = 62*400 - 30*400
=> 50x = 32*400
x=256 L
therefore 256L of solution one is required