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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 Concentration Problem
Solve mixture concentration problems. Find how much of each solution to mix using algebra. Step-by-step guided solution.
Mixture Problem: Orange Juice Blend
Mix 70% and 30% orange juice to get 50%. Find gallons of 70% juice needed. Teaches weighted average method.
Fruit Stand Mixture Problem
Find pounds of raspberries and grapes sold given total revenue and weight. System of two equations.
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.