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
Apr 1, 2016

Answer:

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"#