Question

2. A chemist wants to make 4 liters of a 7% acid solution by mixing a 10% acid solution and a 4% acid solution. How many liters of each solution should the chemist use? Write your answer as a complete sentence Be sure to: (a) Define your variable and expressions for the quantities. (b) Write an equation that models the problem. (c) Solve the equation. (d) State the answer in a complete sentence.

Answer 1

Let $x$ be the number of liters of the 10% solution to be used, and $y$ the number of liters of the 4% solution. The chemist wants to end up with a 4 liter solution, so

$x+y=4$

For each liter used in the mixture, a concentration of either 10% or 4% acid will be contributed, and the goal is to make a 4L solution whose concentration is 7%, which means

$0.1x+0.04y=0.07(x+y)=0.28$

Solving for $x,y$ gives $x=y=2$, so 2L of both solutions is needed.