Question

How many liters each of a 25% acid solution and a 85% acid solution must be used to produce 80 liters of a 40% acid solution? (Round to two decimal places if necessary.)

Answer 1

Step-by-step explanation:

We are given the following information;

25% acid solution + 85% acid solution to derive 80L of 40% acid solution

We shall assign variables to the two different solutions as follows;

`\begin{gathered} a=25\%\text{ solution} \\ b=85\%\text{ solution} \end{gathered}`

Also we can conclude the following;

`a+b=80---(1)`

For the amount of acid contents per solution we will have the following;

`0.25a+0.85b=0.40(80)---(2)`

From equation (1), we can make a the subject and we'll have;

`a=80-b`

Substitute for the value of a into equation (2);

`\begin{gathered} 0.25(80-b)+0.85b=32 \\ 20-0.25b+0.85b=32 \end{gathered}`

Next we collect like terms and simplify further;

`\begin{gathered} 0.85b-0.25b=32-20 \\ 0.6b=12 \end{gathered}`

Divide both sides by 0.6;

`\begin{gathered} (0.6b)/(0.6)=(12)/(0.6) \\ b=20 \end{gathered}`

We can now substitute for b into equation (1);

`\begin{gathered} a+b=80 \\ a+20=80 \\ a=80-20 \\ a=60 \end{gathered}`

Therefore, we now have;

ANSWER:

For the 25% solution = 60 Liters

For the 85% solution = 20 Liters