Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsHard
A chemist is mixing a solution. She needs to combine two solutions, one that is 10% acid and another that is 30% acid, to create 5 liters of a 22% acid solution. How many liters of the 10% acid solution should she use?
- A3 liters
- B3.5 liters
- C2 liters
- D1.5 liters
Show answer & explanationAnswer & explanation
Correct answer: C. 2 liters
Let x be the volume of the 10% solution and y be the volume of the 30% solution. We have two equations: x + y = 5 (total volume) and 0.10x + 0.30y = 0.22(5) (total acid). Solve this system of linear equations.
Why the other options are wrong
- A. Incorrectly solved the system of equations, possibly calculating the 30% solution volume.
- B. Incorrectly solved the system of equations.
- D. Incorrectly solved the system of equations.
System of Linear Equations (Mixture Problems)
Using two or more linear equations to solve problems involving combining different quantities with varying concentrations.
- Typically involves two equations: one for total quantity and one for total amount of a specific component.
- Variables represent the amounts of each substance being mixed.
- Can be solved using substitution or elimination methods.
Memory trick: Total volume, total 'stuff', solve and verify.