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Mixtures Word Problems
Mixture problems involve combining two or more substances with different concentrations, prices, or qualities to achieve a target blend. The classic setup: you have a 40% acid solution and a 70% acid solution, and you need to mix them to get 100 liters of 50% acid. The underlying math is always the same — total amount of the "active ingredient" before mixing equals total after mixing — but the variety of contexts keeps things interesting: blending coffee beans at different price points, mixing alloys with different metal percentages, diluting medication to a target concentration. These problems train you to track a quantity through a transformation, which is a surprisingly transferable skill.
Mixture Problem: Ethanol Fuel Blend
Solve a fuel mixture problem: combine 85% and 25% ethanol to make 50% in 20 gallons. Two methods included.
Mixture Problem: Alcohol Solution
Blend 15% and 30% solutions to make 20%. Set up and solve using concentration equations.
Mixture Problem: Blending Solutions
Solve a two-solution mixture problem using algebraic equations. Find liters needed of each concentration.
Three Acid Solutions Mixture Problem
Mix 20%, 30%, 75% acid solutions to make 48L of 55% acid. Find liters of each with constraint (75% = 2× 30%).
Trail Mix: Weighted Average Price Problem
Paul mixes nuts ($1.25/lb) and oats ($1.65/lb) to make 16 lbs at $1.55/lb. Find pounds of each.
Weighted Average: Percent Defective
Plant A made 12000 panels (6% defective), Plant B made unknown (2% defective). Overall 5% defective. Find Plant B output.