Mixture Problem Workshop

Pre-Algebra · Axiom Academy

Combine two solutions of different strengths into one — and discover the single equation that solves every mixing problem, from acid in a lab to coffee on a shelf. 1. Pouring Two Solutions Into One Mixing isn't magic — it's bookkeeping. Pour a beaker of weak (30%) acid and a beaker of strong (70%) acid into one container. The liquid volumes add , and so does the pure acid hiding inside each. Watch the dark band in each beaker — that's the actual acid — slide together into the final mix. Pure acid is conserved — it just moves from two beakers into one Now solve it without guessing. The whole problem is one balance: acid in equals acid out . Multiply each amount by its concentration, add, and set it equal to the target. amount × concentration, summed, equals total × final concentration Worked example — the acid problem Make 100 mL of 50% acid from a 30% bottle and a 70% bottle. Let x = mL of the 30% solution; then the rest, (100 − x ) , is the 70% solution. 3. The Same Equation, With Prices Swap "concentration" for "price per pound" and nothing else changes. A coffee shop blends an 8/lb roast with a 12/lb roast to make a 10-lb bag that should sell for 10/lb . Total value is conserved exactly the way total acid was. Worked example — the coffee blend Make 10 lb selling at 10/lb. Let x = pounds of the 8 coffee; then (10 − x ) is the 12 coffee. 4. Why the Answer Lands Where It Does

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