Let x l be the amount of 40% alcohol solution and y l be the amount of 80% alcohol solution.
1. Marisol needs 2 liters of a 50% alcohol solution. Then
x+y=2.
2. In x l of 40% alcohol solution is 0.4x l of alcohol, in y l of 80% alcohol solution is 0.8y l of alcohol and in 2 l of 50% alcohol solution is 0.5·2=1 l of alcohol. Then
0.4x+0.8y=1.
2. Solve the system of equations:
[tex]\left\{\begin{array}{l}x+y=2\\0.4x+0.8y=1\end{array}\right.[/tex]
From the first equation
[tex]x=2-y.[/tex]
Substitute it into the second equation:
[tex]0.4(2-y)+0.8y=1,\\ \\0.8-0.4y+0.8y=1,\\ \\0.4y=1-0.8=0.2,\\ \\y=\dfrac{0.2}{0.4}=0.5\ l.[/tex]
Then
[tex]x=2-y=2-0.5=1.5\ l[/tex]
Answer: Marisol should combine 1.5 l 0f 40% alcohol solution with 0.5 l of 80% alcphol solution.
