Final answer:
The problem of determining the volume of two acid solutions with different concentrations mixed to obtain a specific concentration and volume is solved using algebraic equations representing the relationship between concentration and volume of the solutions.
Step-by-step explanation:
To solve the problem of how many liters of 20% and 10% acid should be mixed to obtain 10 liters of 14% acid, one can use the method of algebraic equations derived from the concept of concentration and volume. Let X be the volume in liters of the 20% acid solution, and Y be the volume of the 10% acid solution. The system of equations that represents the problem is:
- X + Y = 10 (the total volume of the mixture is 10 liters)
- 0.20X + 0.10Y = 0.14 × 10 (the total concentration of acid in the mixture)
By solving this system of equations, we find the volume of each acid solution needed. This approach can be applied to other similar problems involving mixtures where the final concentration and volume are known, but the individual volumes contributing to the mixture are unknown.