Answer
The answer is: 4 quarts of solution must be drained and replaced with pure antifreeze.
Work Step by Step
We assign the variable:
x = pure antifreeze added in quarts
Step 1:
Find the equations that represent the problem.
We are mixing both solutions to create a new one,
40% antifreeze + x = 60% antifreeze -> Eq. 1
Remember that since some of the solution is drained, the volume for the 40% antifreeze solution is the total volume minus the drained amount.
40% antifreeze $=0.4(12-x)$ -> Eq. 2
We can get the third equation form the wording in the problem.
From "12-quart cooling system" and "the desired strength of the solution is 60% antifreeze",
60% antifreeze $=0.6(12)=7.2$ -> Eq. 3
Step 2:
Solve the system of equations using the substitution method,
-> Substitute Eq. 2 and Eq. 3 into Eq. 1
$0.4(12-x)+x=7.2$
$4.8-0.4x+x=7.2$
$0.6x=7.2-4.8$
$0.6x=2.4$
$x=\frac{2.4}{0.6}$
$x=4$ qts
Step 3:
The answer is: 4 quarts of solution must be drained and replaced with pure antifreeze.
