GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsHard
A chemist is preparing a solution. They need to mix solution A, which is 15% acid, with solution B, which is 40% acid, to create 100 ml of a 25% acid solution. How many milliliters of solution A should the chemist use?
- A60 ml
- B70 ml
- C50 ml
- D40 ml
Show answer & explanationAnswer & explanation
Correct answer: A. 60 ml
This is a mixture problem that can be solved using a system of two linear equations. One equation represents the total volume, and the other represents the total amount of acid.
Why the other options are wrong
- B. This would result in a solution with too low an acid concentration if mixed with 30ml of B.
- C. This would result in a 27.5% acid solution.
- D. This would result in a solution with too high an acid concentration if mixed with 60ml of B.
Systems of Linear Equations (Mixture Problems)
A problem type where two or more quantities with different concentrations are mixed to form a new quantity with a desired concentration. Solved by setting up equations for total quantity and total amount of a specific component.
- Typically involves two variables and two equations.
- One equation for total volume/weight, another for total amount of substance.
- Can be solved using substitution, elimination, or graphing methods.
Memory trick: Mix Volumes, Match Concentrations.