# 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?

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

#### Explanation:

We have the following situation:

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

where $x = \text{amount of 30% acid", y="amount of 60% acid}$

From this chart, we can see two things:

• $x + y = 50$
• $.3 x + .6 y = .45 \left(50\right)$

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:

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

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

$.3 y = 7.5$

$y = \frac{7.5}{.3}$

$\textcolor{b l u e}{\underline{\overline{\left\mid \textcolor{b l a c k}{\text{y=25}} \right\mid}}}$

which means that:

$x = 50 - 25$

$\textcolor{b l u e}{\underline{\overline{\left\mid \textcolor{b l a c k}{\text{x=25}} \right\mid}}}$