SOLUTION: A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 60 gallons of a 40% solution. How many gallons of the 20% and 50% solution should be m

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Question 1102100: A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 60 gallons of a 40% solution. How many gallons of the 20% and 50% solution should be mixed?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
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