Question

Doreen Schmidt is a chemist. She needs to prepare 28 ounces of a 12% hydrochloric acid solution. Find the amount of 14% soulution and the amount of 7% soulution she should mix to get this soulution.

Answer 1

To prepare the 12% hydrochloric acid solution, Doreen Schmidt needs to mix a 14% solution and a 7% solution. By setting up and solving two equations, the amounts of each solution can be determined.

Step-by-step explanation:

To prepare 28 ounces of a 12% hydrochloric acid solution, Doreen Schmidt needs to mix two different solutions: a 14% solution and a 7% solution. Let's call the amount of 14% solution x and the amount of 7% solution y. We can set up the following equation:

x + y = 28

Next, we can set up another equation based on the concentration of hydrochloric acid in each solution:

0.14x + 0.07y = 0.12(28)

Solving these two equations simultaneously will give us the values of x and y, which represent the amounts of the 14% and 7% solutions respectively that Doreen needs to mix.

Answer 2

now, let's say we'll use "x" oz of the 14% solution, and "y" oz of the 7% solution.

how much hydrochloric acid is there in the "x" oz of 14%? well, is just 14% of x, or (14/100) * x, or 0.14x.

how much hydrochloric acid is there in the "y" oz of 7%? well is just 7% of y, or (7/100) * y, or 0.07y, the rest may be water or some other substance.

now, the mixture needed is 28 oz, and is only 12% of hydrochloric acid, since is 12% hydrochloric acid and the rest water or such, how much hydrochloric acid is there in it? well, is just (12/100) * 28, or 3.36 oz.


`\bf \begin{array}{lccclll} &\stackrel{ounces}{amount}&\stackrel{\%~acid}{quantity}&\stackrel{ounces~acid}{quantity}\\ &------&------&------\\ \textit{14\% sol'n}&x&0.14&0.14x\\ \textit{7\% sol'n}&y&0.07&0.07y\\ ------&------&------&------\\ mixture&28&0.12&3.36 \end{array} \\\\\\ \begin{cases} x+y=28\implies \boxed{y}=28-x\\ 0.14x+0.07y=3.36\\ ----------\\ 0.14x+0.07\left( \boxed{28-x} \right)=3.36 \end{cases} \\\\\\ 0.14x-0.07x+1.96=3.36\implies 0.07x=1.4 \\\\\\ x=\cfrac{1.4}{0.07}\implies x=20`

how many ounces of the 7% solution? well y = 28 - x.