Answer:
The number of liters for container R = x = 0.5 liters
The number of liters for container S = y = 1.5 liters.
Step-by-step explanation:
Let the number of liters of container R = x
Let the number of liters of container S = y
We are told in the question : that
Container R holds a solution that is 20% alcohol
= 20% × x = 0.20x
Container S holds a solution that is 60% alcohol.
= 60% × y = 0.60y
How many liters of solution from each container should be used to create 2 liters of solution that is 50% alcohol?
Hence;
x + y = 2 ....... Equation 1
x = 2 - y
0.20x + 0.60y = 2 × 50%
0.20x + 0.60y = 1........ Equation 2
Substitute
2-y for x in Equation 3
0.20(2 - y) + 0.60y = 1
0.40 - 0.20y + 0.60y = 1
Collect like terms
0.40y = 1 - 0.40
0.40y = 0.60
y = 0.60/0.40
y = 1.5 liters
Note that :
x = 2 - y
x = 2 - 1.5
x = 0.5 liters
Therefore,
the number of liters for container R = x = 0.5 liters
the number of liters for container S = y = 1.5 liters.
