Achemist has one solution containing 30% insecticide and another solution containing 50% insecticide how much of each solution should the chemist mix to get 200l of 42% insecticide?
show your work plz

Let's use L for the 30% insecticide and H for the 50% version.
L + H = 200 liters
0.3L + 0.5H = 0.42(L + H) = 0.42(200) = 84

We notice from the first equation that H = 200 - L (subtracting H from both sides).  So we can substitute this into the second equation to knock out one variable.

0.3L + 0.5(200 - L) = 84 liters
0.3L + 100 - 0.5L = 84 liters [distributive property]
0.3L - 0.5L + 100 = 84 liters [commutative property]
-0.2L + 100 = 84 liters
-0.2L = -16 liters [subtract 100 from each side]
L = 80 [divide both sides by -0.2]

80 + H = 200 from our first equation, so H = 120.

You should make up some of these for yourself and solve them to get the best grasp on the process and improve your understanding.