Question

Doreen Schmidt is a chemist. She needs to prepare 32 ounces of a 12% hydrochloric acid solutionFind the amount of 16% solution and the amount of 8% solution she should mix to get this solution

Answer 1

If Doreen Schmidt is a chemist. She needs to prepare 32 ounces of a 12% hydrochloric acid solution. 16 ounces of the 16% acid solution should be in the mixture.

What is the mixture?

Let x be the ounces of the 16% acid solution.

Equation is: 0.08x+0.16y=0.12(32)

substitute y=32−x into the equation:

0.08x+0.16(32−x)=0.12(32)

Solve for x

0.08x+5.12−0.16x=3.84

Combine like terms:

−0.08x+5.12=3.84

Subtract 5.12 from both sides:

−0.08x=−1.28

Divide by −0.08:

x= −1.28/−0.08

x =16

Therefore 16 ounces of the 16% acid solution should be in the mixture.

Answer 2

ANSWER: 16 ounces of the 11% solution and 12 ounces of the 7% solution should be used.

Explanation: Let x be the number of ounces of the 14% solution and 28 - x be the number of ounces of the 7% solution.

The equation you must set up shows the number of ounces of acid added from each solution equals the number of ounces in the 11% solution.

The key thing to remember is that the number of ounces of acid is the amount of solution times the concentration of acid it contains.

Thus,

.11x + .07(28-x) = .11(28).

You can solve this in the usual way, but it helps to clear the decimals by multiplying both sides by a suitable number.

So here goes,

.14x + 1.96 - .07x = 3.08

Multiply both sides by 100:

14x + 196 - 7x = 308.

Now finish solving:

7x = 308 - 196 = 112
x = 112/7 = 16

Then 28-x = 28 - 16 = 12.