Answer
The answer is: the volume of pure alcohol to be added must be 375mL.
Work Step by Step
We assign the variable:
x = volume of pure alcohol
Step 1:
Find the equations that represent the problem.
We are mixing both solutions to create a new one,
40% solution + x = 60% solution -> Eq. 1
We can get the second equation form the wording in the problem.
From "750 mL of a solution that is 40% alcohol",
40% solution $=0.4(750)=300$ -> Eq. 2
We can get the third equation form the wording in the problem.
From "to make a solution that is 60% alcohol",
60% solution $=0.6(x+750)=300$ -> Eq. 3
(Remember the volume from the new solution has to equal the sum of both volumes of the initial solutions.)
Step 2:
Solve the system of equations using the substitution method:
-> Substitute Eq. 2 and Eq. 3 into Eq. 1
$300+x=0.6(x+750)$
$300+x=0.6x+450$
$x-0.6x=450-300$
$0.4x=150$
$x=\frac{150}{0.4}$
$x=375$ mL
Step 3:
The answer is: the volume of pure alcohol to be added must be 375mL.
