A chemist wants to mix an 8% salt solution with a 20% salt solution to obtain 12 liters of an 18% salt solution. How much of the 20% solution should she use? a. 9 liters of the 20% solution
b. 6 liters of the 20% solution
c. 10 liters of the 20% solution
d. 2 liters of the 20% solution

C: 10 L of the 20% solution

Let

x = amount of 8% solution

y = amount of 20% solution

The chemist wants to end up with a 12-L mixture, so

x + y = 12

x L of 8% solution contains 0.08x L of salt, and y L of 20% solution contains 0.2y L of salt. When combined, the resulting mixture should have a concentration of 18% salt, or 18% of 12 L = 2.16 L of salt, so

0.08x + 0.2y = 2.16

Solve for y :

x = 12 - y

0.08 (12 - y) + 0.2y = 2.16

0.96 - 0.08y + 0.2y = 2.16

0.12y = 1.2

y = 10