Respuesta :
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;
[tex]\begin{gathered} a=25\%\text{ solution} \\ b=85\%\text{ solution} \end{gathered}[/tex]Also we can conclude the following;
[tex]a+b=80---(1)[/tex]For the amount of acid contents per solution we will have the following;
[tex]0.25a+0.85b=0.40(80)---(2)[/tex]From equation (1), we can make a the subject and we'll have;
[tex]a=80-b[/tex]Substitute for the value of a into equation (2);
[tex]\begin{gathered} 0.25(80-b)+0.85b=32 \\ 20-0.25b+0.85b=32 \end{gathered}[/tex]Next we collect like terms and simplify further;
[tex]\begin{gathered} 0.85b-0.25b=32-20 \\ 0.6b=12 \end{gathered}[/tex]Divide both sides by 0.6;
[tex]\begin{gathered} \frac{0.6b}{0.6}=\frac{12}{0.6} \\ b=20 \end{gathered}[/tex]We can now substitute for b into equation (1);
[tex]\begin{gathered} a+b=80 \\ a+20=80 \\ a=80-20 \\ a=60 \end{gathered}[/tex]Therefore, we now have;
ANSWER:
For the 25% solution = 60 Liters
For the 85% solution = 20 Liters
