Transferring handicaps across different game lengths: In an 80-point game, A gives B 5 points and C 15 points. In a 60-point game, how many points can B give C?

Introduction / Context:Point handicaps correspond to speed ratios. Once we deduce relative speeds of A, B, and C from one game length, we can project the handicap to any other length by proportional scoring speed.

Given Data / Assumptions:

• In 80-point game: A vs B → A: B = 80 : 75 = 16 : 15.
• In 80-point game: A vs C → A: C = 80 : 65 = 16 : 13.
• Uniform scoring speeds; linear scaling.

Concept / Approach:From A: B = 16 : 15 and A: C = 16 : 13 ⇒ B : C = 15 : 13. In a 60-point game, when C reaches 60, B would reach (15/13)*60; or equivalently, when B reaches 60, C would be at (13/15)*60.

Step-by-Step Solution:

Verification / Alternative check:Alternatively, at C = 60, B = 60 * (15/13) ≈ 69.23, meaning B is 9.23 ahead at C's 60; rounded handicap in B's frame at total 60 for B is exactly 8 points given to C.

Why Other Options Are Wrong:6/10/12 don’t match the precise 15:13 ratio at 60 points.

Common Pitfalls:Assuming differences transfer linearly; it’s the ratio that transfers, not absolute gap.

Final Answer:8