Handicap conversion between B and C: In a 160-point game, A gives B 10 and A gives C 30. In a game to 60, how many can B give C?

Introduction / Context:
Translate handicaps into scoring ratios and then deduce B:C. Finally scale a 60-point game to find the start B can give C.

Given Data / Assumptions:

• A:B = 160:150 = 16:15
• A:C = 160:130 = 16:13
• Target game size = 60

Concept / Approach:
B:C = (A:C)/(A:B) = (16/13)/(16/15) = 15/13. When B scores 60, C gets 60*(13/15). The difference is B’s start to C.

Step-by-Step Solution:

Verification / Alternative check:
Ratios are consistent with both handicaps from A.

Why Other Options Are Wrong:
They contradict B:C = 15:13 scaling to 60 points.

Common Pitfalls:
Subtracting point handicaps directly instead of using ratios.

Final Answer:
8