Question

doreen schmidt is a chemist. she needs to prepare 24 ounces of a 9% hydrochloric acid solution. find the amount of 12% solution and the amount of 6% solution she should mix to get this solution.
first solution second solution mixture needed
concentration 6% 12% 9%
ounces of solution x y 24
ounces of pure acid 0.06x 0.12y 0.09(24)
how many ounces of the 12% acid solution should be in the mixture?
how many ounces of the 6% acid solution should be in the mixture?

Explanation:

Step1: Set up equations

Let $x$ be the amount of the 6% acid solution and $y$ be the amount of the 12% acid solution. We know two - equations: $x + y=24$ (total volume equation) and $0.06x + 0.12y=0.09\times24$ (acid - content equation).

Step2: Solve the first equation for $x$

$x = 24 - y$

Step3: Substitute $x$ into the second equation

$0.06(24 - y)+0.12y=0.09\times24$
$1.44-0.06y + 0.12y=2.16$
$0.06y=2.16 - 1.44$
$0.06y = 0.72$
$y=\frac{0.72}{0.06}=12$

Step4: Find $x$

Substitute $y = 12$ into $x = 24 - y$, we get $x=24 - 12 = 12$

Answer:

12 ounces of the 6% acid solution and 12 ounces of the 12% acid solution should be in the mixture.