Answer
The answer is: 20 liters of regular milk.
Work Step by Step
We assign the variable:
x = liters of regular milk
Step 1:
Find the equations that represent the problem.
We are mixing both solutions to create a new one,
4% solution + 1% solution = 2% solution -> Eq. 1
We can get the second equation from the wording in the problem.
From "Regular milk has 4% butterfat",
4% solution $= 0.04x$ -> Eq. 2
We can get the third equation from the wording in the problem.
From "40 L of milk with 1% butterfat ",
1% solution $= 0.01(40)=0.4L$ -> Eq. 3
We can get the fourth equation from the wording in the problem.
From "litres of regular milk must be mixed with 40 L of milk with 1% butterfat to have milk with 2% butterfat",
2% solution $= 0.02(x+40)$ -> Eq. 4
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute Eq. 2, Eq. 3 and Eq. 4 into Eq. 1
$0.04x+0.4=0.02(x+40)$
$0.04+0.4=0.02x+0.8$
$0.04x-0.02x=0.8-0.4$
$0.02x=0.4$
$x=\frac{0.4}{0.02}$
$x=20$
Step 3:
The answer is: 20 liters of regular milk.
