Solve the problem by setting up and solving a system of two linear equations in two variables. Use either the elimination-by-addition or the substitution method to solve the system. One solution contains 20% alcohol and a second solution contains 30% alcohol. How many liters of each solution should be mixed to make 10 liters containing 26% alcohol?
A) 5 liters of 20% and 5 liters of 30%
B) 4 liters of 20% and 6 liters of 30%
C) 2 liters of 20% and 4 liters of 30%
D) 6 liters of 20% and 4 liters of 30%
E) none of these

Question

Quizplus · Accepted Answer

Let $x$ be the liters of 20% alcohol solution and $y$ be the liters of 30% alcohol solution. The system of equations is:1. $x + y = 10$ (total liters)2. $0.20x + 0.30y = 0.26 \times 10$ (total alcohol content)Solving this system, we find $x = 4$ and $y = 6$, meaning 4 liters of 20% solution and 6 liters of 30% solution are needed.

Solve the Problem by Setting Up and Solving a System