We want to create 50 liters of 45% concentrated acid. We have two solutions - one is 30% acid and the other is 60% acid. How much of each is needed to create our desired solution?

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Answer 1 · 2017-02-08T11:34:18

25 litres of each of the 30% and 60% solutions will produce the required 50 litres of 45% acid

We have the following situation:

$((color(white)(000),litres, acid %),("want",50,45%),("have",x,30%),("have",y,60%))$

where $x="amount of 30% acid", y="amount of 60% acid"$

From this chart, we can see two things:

To solve, I'm going to take the first equation and solve for $x$ in terms of $y$ :

$x=50-y$

and now substitute it into the second equation:

$.3(50-y)+.6y=.45(50)$

$15-.3y+.6y=22.5$

$.3y=7.5$

$y=7.5/.3$

$color(blue)ul( bar( abs( color(black)("y=25"))))$

which means that:

$x=50-25$

$color(blue)ul( bar( abs( color(black)("x=25"))))$