Question

A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10 liters of a 20% alcohol solution?

Answer 1

Let x=volume of 18% solution.
Use formula c1v1+c2v2=cv
c1=18%
c2=40%
c=20%
v=10 L
v1=x L
v2=10-x L

Apply formula
0.18x+0.40(10-x)=0.20(10)
expand
0.18x+4-0.40x = 2
solve
4-2=0.22x
x=2/0.22
=100/11
=9.091 L  (to 3 decimal places)

Answer: 9.091 L of 18%, and (10-9.091)=0.909 L of 40%

Check:
c1v1+c2v2=0.18(9.091)+0.40(0.909)=2 
cv=0.2*10 =  2   ok