Question

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?

Answer 1

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="amount of 30% acid", y="amount of 60% acid"`

From this chart, we can see two things:

• `x+y=50`
• `.3x+.6y=.45(50)`

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"))))`