Mixture Problems
📋 What it is
Mixture problems track the AMOUNT of the pure ingredient, not just the total volume.
🗣️ Coach says
In “mix a 20% and a 50% solution,” don’t track the liquid — track the pure STUFF inside. 2 litres of 20% has 0.4 L of the ingredient. Add the pure amounts, then divide by the total volume for the final strength.
🧠 Memory hook
Track the PURE ingredient (amount = volume × strength), not just the total liquid.
😂 Giggle
Why did the reckoner love the number 100?
Because everything is easier when you can lean on a round friend!
😲 Whoa!
Mixture maths runs the real world — pharmacists mixing medicine doses, chefs balancing flavours, and factories blending fuels all use exactly this “track the pure amount” idea.
✅ Quick check: How much pure salt is in 2 L of a 25% salt solution?
Say your answer out loud first — then reveal.
✏️ Check your work Re-multiply volume × strength for each part, add the pure amounts, then divide by the TOTAL volume — does your final strength land BETWEEN the two you mixed?
0.5 L — amount = volume × strength = 2 × 0.25 = 0.5 L of pure salt.
The pure-ingredient amount is volume times concentration; that’s what you track.
🧪 Try it! (2 minutes)
If juice is 10% sugar, how much sugar is in 500 mL? (500 × 0.10 = 50 mL.) Track the pure part.
🔎 How did you work this?