To find liter’s of each solution required to obtain desired mixture
Answer to Problem 15CT
The 25 liters of 20% solution is mixed with 75 litres of 60% solution to obtain 100 liters of a 50% solution to get the desired mixture.
Explanation of Solution
Given:
One hundred litres of a 50% solutions is obtained by mixing 60% solution with a 20% solution.
Let x litres of 20% solution is mixed with y liters of 60% solution to obtain 100 liters of a 50% solution.
Then, the amount of solute as:
This equation can also be rewritten as:
Now, the total volume of the mixture is 100 liters.
So,
Now, the system of linear equations is:
Here, the augmented matrix is:
The system can be solved by Gauss-Jordan elimination.
The reduced row-echelon form is obtained by the row transformations as:
So,
So, the solution of the system of linear equations is
Hence, 25 liters of 20% solution is mixed with 75 litres of 60% solution to obtain 100 liters of a 50% solution.
Chapter 8 Solutions
EBK PRECALCULUS W/LIMITS
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