Solution A is 60% alcohol and Solution B is 30% alcohol. How much of each is needed to make 30 gallons of a solution that is 40% alcohol

Answer 1

A + B = 30
0.6A + 0.3B = 0.4(30)

A + B = 30
6A + 3B = 120

-3A -3B = -90
6A + 3B = 120

3A = 30
3A/3 = 30/3
A = 10
10 + B = 30
10-10 + B = 30-10
B = 20

Or
A = x B = 3-x , 0.4(30)
0.6x + 0.3(30-x) = 0.4(30)
0.6x + 9 -0.3x = 12
0.3x + 9 = 12
0.3x + 9-9 = 12-9
0.3x = 3
0.3x/0.3 = 3/0.3
x = 10
A = 10
B =30-10 =20
10 at 60% and 20 at 30%.