Define a variable for each of the two given solutions. What is the amount of insecticide per liter in each solution?
30 % Insecticide Solution to Be Used: 80 L 50 % Insecticide Solution to Be Used: 120 L
Practice makes perfect
Let's start by defining variables that represent the amounts of each of type of solution to be used.
& x = number of liters of 30 % insecticide solution
& y = number of liters of 50 % insecticide solution
Since the chemist wants to mix the solutions, it implies that both x and y add to be 200.
x + y=200
Now, let's make a table where we can see how much insecticide is contained in each solution per liter used.
% of Insecticide
Total (L)
Part Insecticide (L)
Solution 1
30
x
0.3* x
Solution 2
50
y
0.5* y
Final Mix
42
200
0.42* 200
Now, since we want to mix Solutions 1 and 2 in such a way that we will get the Final Mix, the blue and green amounts have to add to be the red amount.
0.3* x + 0.5* y = 0.42* 200
Therefore, we have a system of linear equations that models the described situation.
x+y=200 & (I) 0.3x+0.5y=0.42* 200 & (II)
In order to solve this system, we can use the Substitution Method. First, let's solve the first equation for y.
This implies that the chemist has to mix 80 L of the 30 % insecticide solution with 120 L of the 50 % insecticide solution to obtain 200 L of a 42 % insecticide solution.
