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.Mix two alloys (25% and 50% copper) to make 500g at 45% copper. Use systems of equations to find quantities.
Solve a two-alloy mixture problem using percent composition. Two equations, two unknowns with weighted averaging.
Find how much fluid to drain and replace with pure antifreeze to change concentration from 30% to 60%.
Find count of pennies, dimes, quarters given total coins, total value, and constraint on dime-quarter relationship.
Solve a fuel mixture problem: combine 85% and 25% ethanol to make 50% in 20 gallons. Two methods included.
Use proportional reasoning to find volume per marble and calculate water needed with different marble counts.
Blend 15% and 30% solutions to make 20%. Set up and solve using concentration equations.
Juan mixes two alcohol solutions (17% and 14%). Solution A is 500 mL less than B. Final mix has 335 mL pure alcohol. Find volume of B.
Find pounds of 55% silver alloy mixed with 30% alloy to create 40% alloy. Solve mixture concentration with weighted averages.
Solve a two-solution mixture problem using algebraic equations. Find liters needed of each concentration.