A 27 quartz capacity car radiator is filled with 18\% alcohol solution. How many quartz be drained and then be replaced by a 90\% alcohol solution for resulting solution to contain 42\% alcohol?
(a)7 quartz
(b)9 quartz
(c)11 quartz
(d)14 quartz
Answer
Answer (as printed): B
Explanation
Let $x$ quartz of the first solution be drained and replaced by $x$ quartz of the second solution. Then, 18\% of $(27-x)+90 \%$ of $x=42 \%$ of 27 $$\begin{aligned} & \Rightarrow \quad 18(27-x)+90 x=42 \times 27 \\ & \Rightarrow \quad 486-18 x+90 x=1134 \\ & \Rightarrow \quad 72 x=648 \\ & \Rightarrow \quad x=9 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.