Question

Marie mixes 20 liters of 12% acid solution with a 36% acid solution to make a 20% acid solution. How many liters of 36% solution did she use?

Answer 1

Use c1v1+c2v2=c3v3
where c=concentration, v=volume.

C1=0.12
V1=20 L
C2=0.36
V2=X
C3=0.20
V3=20+X L

Substitute in equation
0.12(20) + 0.36X = 0.20(20+X)
Expand
2.4 + 0.36X = 4 + 0.2X
Simplify
(0.36-0.2)X = 4-2.4
0.16X = 1.6
X=1.6/0.16 = 10 L

check:
0.12(20)+0.36(10)=2.4+3.6=6.0
(20+10)*0.20 = 6.0 so solution is good.

Answer: Volume of 36% solution is 10L