Misconceptions & Reasoning
📋 What it is
Common traps: adding ratios wrongly, confusing percent of vs percent change, ignoring the base.
🗣️ Coach says
Ratio traps are sneaky. You can't just add ratios (2:3 + 1:2 ≠ 3:5). "20% off then 20% off" isn't 40% off. And a percent means nothing without its base. Naming these traps keeps you accurate.
🧠 Memory hook
You can't add ratios directly. Two 20%-offs ≠ 40% off. A percent needs its base.
😂 Giggle
Why did the constant of proportionality feel important?
Because without it, the whole relationship falls apart — it's literally the k that holds everything together!
😲 Whoa!
Two successive "20% off" discounts give only 36% off total — a trap that fools shoppers every day.
✅ Quick check: A $100 item gets 20% off, then another 20% off. Is that 40% off?
Say your answer out loud first — then reveal.
No — $100 → $80 → $64, which is 36% off total.
The second discount applies to the already-reduced price, not the original.
🪄 Trick question: Does "50% more" then "50% less" bring you back to the start?
Careful — think it through, then reveal.
No — 100 → 150 → 75; you end up lower.
The second percent acts on a different (larger) base, so they don't cancel.
🧪 Try it! (2 minutes)
Prove it: take $100, apply 20% off twice, and check the total isn't $60.