Digital SATMath: AlgebraMedium
A chemist is preparing a solution by mixing two different concentrations of acid. Solution A is 15% acid, and Solution B is 40% acid. The chemist wants to produce 500 mL of a 25% acid solution. Let 'a' be the volume of Solution A in mL and 'b' be the volume of Solution B in mL. Which system of equations can be used to find the volumes of Solution A and Solution B needed?
- Aa + b = 500 0.15a + 0.40b = 0.25(500)
- Ba + b = 0.25 0.15a + 0.40b = 500
- Ca + b = 500 0.15a + 0.40b = 0.25
- D0.15a + 0.40b = 500 a + b = 0.25(500)
Show answer & explanationAnswer & explanation
Correct answer: A. a + b = 500 0.15a + 0.40b = 0.25(500)
The first equation represents the total volume: the sum of the volumes of Solution A and Solution B must equal 500 mL (a + b = 500). The second equation represents the total amount of acid: 15% of 'a' plus 40% of 'b' must equal 25% of the total 500 mL (0.15a + 0.40b = 0.25 * 500).
Why the other options are wrong
- B. Both equations are incorrectly formulated; the total volume is 500, and the acid amount is 0.25 * 500.
- C. The second equation incorrectly equates the total acid amount to just the target concentration, not the amount of acid in the final solution.
- D. Both equations are incorrectly formulated, swapping volumes and concentrations, and miscalculating total acid.
System of Linear Equations (Mixture Problems)
Mixture problems involve combining two or more quantities with different properties to create a desired mixture. They are typically solved using a system of two linear equations.
- One equation represents the total amount/volume of the mixture.
- The second equation represents the total amount of the key component (e.g., acid, solute) in the mixture.
- Convert percentages to decimals for calculations.
Memory trick: Mix it Up: Total amount equation, then total component equation!