Question

Doreen Schmidt is a chemist. She needs to prepare 32 ounces of a 13​% hydrochloric acid solution. Find the amount of 16​% solution and the amount of 8​% solution she should mix to get this solution.

Answer 1

Answer:

She should mix 20 ounces of 16% solution and 12 ounces of 8% solution.

Step-by-step explanation:

Given:

Doreen Schmidt needs to prepare 32 ounces of a 13​% hydrochloric acid solution.

Now, to find the amount she should mix of 16% solution and of 8% solution.

Let the 16% solution amount be $x.$

And let the 8% solution amount be $y.$

So, the total ounces of solution:

$x+y=32$

$y=32-x$ .......(1)

Now, to solve the equation to get the solution she should mix:

$16\%\ of\ (x)+8\%\ of\ (y)=13\%\ of\ (32)\\\\\frac{16}{100}\times x+\frac{8}{100}\times y=\frac{13}{100}\times 32$

$0.16x+0.08y=0.13\times 32$

Substituting the value of $y$ from equation (1) we get:

$0.16x+0.08(32-x)=4.16$

$0.16x+2.56-0.08x=4.16$

$2.56+0.08x=4.16$

Subtracting both sides by 2.56 we get:

$0.08x=1.6$

Dividing both sides by 0.08 we get:

$x=20.$

The 16% solution amount = 20 ounces.

Now, substituting the value of $x$ in equation (1) we get:

$y=32-x\\\\y=32-20\\\\y=12.$

The 8% solution amount = 12 ounces.

Therefore, she should mix 20 ounces of 16% solution and 12 ounces of 8% solution.