Let A denote the 50% solution and B denote the 20% solution which we have.
Let C denote the 40% solution which we want.
Using the method of alligation.
50 20 20/30*60=40 gal of 50% solution
40 40+20= 60 gal of 40% solution
20 10 10/30*60=20 gal of 20% solution
30
10= 50 - 40
20= 40 - 20
20+10=30 parts total
There are 60 gal total
50 20 20/30*60=40 gal of 50% solution
20/30*60=40
40 gal of 50% solution.
60-40=20 gal
20 10 10/30*60=20 gal of 20% solution
20 gal of 20% solution.
check
0.2 * 20 + 0.5 * 40 = 0.4*60
4.0 + 20.0 = 24.0
24.0 = 24.0
ok
Now using algebra
We need a total of 60 gal at 40%
We want to know how many gal at 20% to mix with 50%
a+b=60
0.2*a+0.5*b=0.4*60
a=60-b
0.2*(60-b)+0.5*b=24
12-0.2b+0.5*b=24
0.3*b=12
b=40
a=60-b
a=20 gal at 20%
b=40 gal at 50%
check
0.2*20+0.5*40=0.4*60
4+20=24
24=24
ok
codemx1