Sum & Ratio

1. 1The Equal PartsThe parts land one by one: quantity A has 3 sky-blue parts and quantity B has 2 violet parts. A ratio does not count values — it counts equal parts.3 parts + 2 parts
2. 2Bracket the Combined SumBoth quantities together make 40, so the 5 equal ratio units must share that total.Total Sum = 40
3. 3Count the Equal PartsA gold light walks the parts and counts them: 3 parts of A, then 2 parts of B — 5 equal parts in all.3 + 2 = 5 equal parts
4. 4Find the Value of One Part FirstFind the value of one part first: share the total of 40 equally across the 5 parts we just counted. Each part is worth 40 ÷ 5 = 8.1 part = 40 ÷ 5 = 8
5. 5Solve for Quantity ASweep A's 3 parts while the counter adds one part-value at a time: a = 24.a = 3 × 8 = 24
6. 6Solve for Quantity BSweep B's 2 parts the same way: b = 16.b = 2 × 8 = 16
7. 7Check the AnswerAdd the two answers back: 24 + 16 = 40 — the given total. Common mistake: dividing the total 40 by 3 (only A's parts) to find one part — you must divide by the total parts 5.24 + 16 = 40 ✓
8. 8Summary & DiagnosisGiven the SUM → add the parts. Given the DIFFERENCE → subtract the parts. Facing a new problem, the first question is: what are you given?a = 24, b = 16

Change the numbers to test the engine with any sum & difference problem: