# A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 L of a solution containingg 42% insecticide. How much of each solution should be used?

##### 1 Answer

#### Explanation:

the final mixture will have a capacity of

this means that the final mixture will have

the first solution has a certain capacity which we can denote as

we know that the capacity of insecticide in the first solution is

this can be written as

we know that the capacity of insecticide in the second solution is

this can be written as

we then know that

this can be written as

we also have the equation

we can then make the

using the method of elimination for simultaneous equations (where you subtract the two):

subtracted with

gives

or

multiplying both sides by

meaning that

we can then substitute the value for

to check, you can find the capacities of each insecticide and see whether they add to

so the answers make sense.