Let the amount of 30% acid solution be a
Let the amount of 60% acid solution be b
Given, "a" and "b" mixed together gives 570 liters of 31% acid. We can write:
[tex]0.3a+0.6b=0.31(570)[/tex]Also, we know 30% acid and 60% acid amounts to 570 liters, thus:
[tex]a+b=570[/tex]The first equation becomes:
[tex]0.3a+0.6b=176.7[/tex]We can solve the second equation for a:
[tex]\begin{gathered} a+b=570 \\ a=570-b \end{gathered}[/tex]Putting this into the first equation, we can solve for b. The steps are shown below:
[tex]\begin{gathered} 0.3a+0.6b=176.7 \\ 0.3(570-b)+0.6b=176.7 \\ 171-0.3b+0.6b=176.7 \\ 0.3b=176.7-171 \\ 0.3b=5.7 \\ b=\frac{5.7}{0.3} \\ b=19 \end{gathered}[/tex]So, a will be:
a = 570 - b
a = 570 - 19
a = 551
Thus,
551 Liters of 30% acid solution and 19 Liters of 60% acid solution need to be mixed.
