MATH STRATEGY GUIDE

Solving Mixture Problems

The Golden Equation

Most SAT mixture problems involve combining two solutions to reach a final concentration. The key formula is:

(C1 × Q1) + (C2 × Q2) = Cf × Qtotal

The 3-Step Method

  • Define Variables: Let x be the amount of the first substance and y be the amount of the second.
  • Set Up the Table: Create columns for Percent/Price, Amount, and Total Value.
  • Build the System: Usually, you need two equations—one for the total volume (x + y = Total) and one for the mixture components.

Example Problem

A chemist has 10 liters of a 20% saline solution. How many liters of a 50% saline solution must be added to create a mixture that is 30% saline?

Setup:
(0.20 × 10) + (0.50 × x) = 0.30(10 + x)
2 + 0.50x = 3 + 0.30x
0.20x = 1
x = 5

Result: 5 Liters

Pro Tip: When mixing a substance with pure water, the concentration of the "active" ingredient in water is 0%. If adding "pure" substance, the concentration is 100%.