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?

1 Answer
Michael
Apr 1, 2016

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"

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