In a 100-point game, A can give B 20 points and C 28 points. How many points can B give C (in a 100-point game)?

Given data

• On a 100-point game scale: when A scores 100, B scores 80 (A gives B 20 points).
• When A scores 100, C scores 72 (A gives C 28 points).

Concept/ApproachUse relative strengths: A : B : C = 100 : 80 : 72 ⇒ B : C = 10 : 9. If B plays to 100, C will score proportionally 90; hence B can spot C (100 − 90) points.

Step-by-step calculationB : C = 80 : 72 = 10 : 9If B's target = 100, then C's corresponding score = 100 × (9/10) = 90Points B can give C = 100 − 90 = 10 points

Verification/AlternativeCheck transitivity: A:B = 100:80 and A:C = 100:72 ⇒ B:C = (80:72) = 10:9, consistent.

Common pitfallsSubtracting given advantages directly (20 − 28) instead of using ratios; always compare via common baseline.

Final Answer10 points