Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A chemist is mixing a solution. She needs to combine two solutions, one that is 10% acid and another that is 30% acid. If she wants to make 5 liters of a 22% acid solution, how many liters of the 10% acid solution should she use?
- A2 liters
- B3 liters
- C1.5 liters
- D2.5 liters
Show answer & explanationAnswer & explanation
Correct answer: A. 2 liters
Let x be the amount of the 10% acid solution and y be the amount of the 30% acid solution. We can set up a system of two linear equations based on the total volume and the total amount of acid.
Why the other options are wrong
- B. This is the amount of the 30% solution needed if the answer was 2 liters for the 10% solution (5 - 2 = 3).
- C. This is (5 * 0.22 - 5 * 0.30) / (0.10 - 0.30), which is incorrect. Or a miscalculation of 2.75 / 1.5.
- D. This is exactly half of the total volume, implying equal parts, which won't result in 22%.
System of Linear Equations (Mixture Problems)
Mixture problems involve combining two or more quantities with different concentrations to achieve a desired final concentration; solved using a system of linear equations.
- One equation for total quantity.
- Another equation for total amount of specific component (e.g., acid, solute).
- Solve using substitution or elimination.
Memory trick: Volume Plus Concentration Equals Solution.