The current 82% applies to the completed 70% of the course, not to all 100%. Its whole-course contribution is therefore 82 × 0.70 = 57.4 points. To reach 85 points overall, the final must add 27.6 points. Since the final controls 30 points at most, dividing the needed contribution by 0.30 reveals the required exam percentage.
Solve the 27.6-point gap
The equation is 57.4 + final × 0.30 = 85. Subtract 57.4 to obtain final × 0.30 = 27.6, then divide by 0.30: final = 92. The answer is within the 0%–100% range, so the target is arithmetically reachable. A 92% exam contribution is 27.6 points, and 57.4 + 27.6 checks exactly to 85.
Compare expected and endpoint scenarios
If the expected exam score is 80%, the predicted course grade is 57.4 + 80 × 0.30 = 81.4%. A zero on the final produces the minimum 57.4%; a perfect final produces the maximum 87.4%. These endpoints explain why 85% is possible but demanding. They do not account for curves, bonuses, rounding, or policies outside the stated weights.