In a 250-point game, A can give B 50 points and C 70 points. In the same game, how many points can B give C?

Introduction / Context:Head starts over a common target convert into scoring rate ratios. From A's advantages over B and C to 250 points, deduce B's advantage over C for the same target.

Given Data / Assumptions:

• When A scores 250, B scores 200 ⇒ A:B = 250:200 = 5:4.
• When A scores 250, C scores 180 ⇒ A:C = 250:180 = 25:18.

Concept / Approach:Compute B/C = (B/A)/(C/A) = (4/5)/(18/25) = 10/9. If B scores 250, C scores 250*(9/10) = 225, so B can give C a 25-point start to 250.

Step-by-Step Solution: B/A = 4/5; C/A = 18/25 B/C = (4/5) / (18/25) = 10/9 C's score when B reaches 250 = 250*(9/10) = 225 Start B gives C to 250 = 250 − 225 = 25 points

Verification / Alternative check:Scaling down to 100 points would yield 10 points; scaling to 250 multiplies by 2.5, giving 25, consistent with proportional rates.

Why Other Options Are Wrong:18, 20, 22 do not correspond to the 10:9 ratio at a 250-point target.

Common Pitfalls:Adding/subtracting the given head starts directly; not converting starts to rate ratios first.

Final Answer:25 points