Advanced Synthesis
📋 What it is
The capstone: a multi-step real problem chaining ratios, proportions and percents.
🗣️ Coach says
Everything comes together: read a real situation, scale with a proportion, convert with a rate, adjust with a percent, and check. Synthesis is running that whole chain cleanly and picking the right tool each step.
🧠 Memory hook
Scale → convert → adjust → check. One clean chain of ratio-reasoning.
😂 Giggle
Why did the tax rate make everyone nervous?
Because it always takes a percentage off the top!
😲 Whoa!
Planning a big event — food, budget, seating — is pure ratio-and-percent synthesis at scale.
✅ Quick check: Cater a 2:1 snack ratio for 30 people within a budget with 10% tax. Outline the steps.
Say your answer out loud first — then reveal.
Scale the ratio to 30 (proportion), price it (rate), add 10% tax (percent), check the budget.
Synthesis chains proportion, rate and percent into one plan.
🧪 Try it! (2 minutes)
Plan snacks for 12 friends at a 3:1 ratio, then add 10% extra. Use a proportion then a percent.