Question

A chemist has one solution containing 30% insecticide and another solution containing 50% insecticide. How much of each solution should the chemist mix to get 200 L of a 42% insecticide?

Answer 1

He or she should use `79.6"L"` of the `30%` solution and `120.4"L"` of the `50%` solution.

Explanation:

Amount of substance = concentration x volume.

Let `x` = the volume of the `30%` solution.

Let `y` = the volume of the `50%` solution.

Because the total amount of insecticide does not change
we can set up 2 simultaneous equations:

`(200xx42)=(30xxx)+(50xxy)" "color(red)((1))`

`x+y=200" "color(red)((2))`

`color(red)((1))` becomes:

`8400=30x+50y`

From `color(red)((2))`:

`x=200-y`

Substitute this for `x` into `color(red)((1))rArr`

`8400=30(200-y)+50y`

`8400=6000-30y+50y`

`2408=20y`

`y=2408/20=120.4"L"`

Substitute this back into `color(red)((2))rArr`

`x=200-120.4=79.6"L"`