Question

What quanity of 80 percent acid solution must be mixed with a 20 percent solution to produce 840 mL of a percent solution? mL of acid solution

Answer 1

We need to mix a quantity "x" of 80 percent acid with a quantity "y" of 20 percent acid to produce 840 ml of with 50 pct acid.

The first step to solve it is to calculate how much acid we need on the final solution, since it's 50%, then half of its volume must be of acid as shown below:

`\text{total acid=840}\cdot(50)/(100)=840\cdot0.5=420`

We need to mix the solutions in a way that their total volume is equal to 840 ml, while the sum of the volume of acid in each is equal to 420 ml.

`\begin{gathered} x+y=840 \\ 0.8\cdot x+0.2\cdot y=420 \end{gathered}`

To solve this system we first need to multiply the first equation by -0.2:

`\begin{gathered} -0.2\cdot x-0.2\cdot y=-168 \\ 0.8\cdot x+0.2\cdot y=420 \end{gathered}`

We can then add both equations to eliminate one variable.

`\begin{gathered} -0.2\cdot x+0.8\cdot x=-168+420 \\ 0.6\cdot x=252 \\ x=(252)/(0.6)=420 \end{gathered}`

To find the value of y we need to replace x by the calculated value above.

`\begin{gathered} 0.8\cdot420+0.2\cdot y=420 \\ 336+0.2\cdot y=420 \\ 0.2\cdot y=420-336 \\ 0.2\cdot y=84 \\ y=(84)/(0.2)=420 \end{gathered}`

We need 420 ml of the 80% acid solution and 420 ml of the 20% acid solution.