What you need on the final for an 80 overall: solved step by step

Problem. Your current grade is 72% and covers the 60% of the course that is not the final exam, which is worth 40%. The overall grade is 0.6 × (current) + 0.4 × (final), and you want to know what final score F gives an overall 80% and what gives a bare pass at 50%.

Step by step

1. Write the formula: overall = 0.6 × 72 + 0.4 × F. The 0.6 and 0.4 are the weights of the coursework and the final.

2. Work out the part you already have: 0.6 × 72 = 43.2 points toward the overall grade.

3. For an 80 overall, set up 43.2 + 0.4 × F = 80.

4. Subtract 43.2 from both sides: 0.4 × F = 80 − 43.2 = 36.8.

5. Divide both sides by 0.4: F = 36.8 ÷ 0.4 = 92. You need 92% on the final.

6. For a bare pass at 50, set up 43.2 + 0.4 × F = 50, so 0.4 × F = 50 − 43.2 = 6.8.

7. Divide by 0.4: F = 6.8 ÷ 0.4 = 17. You need 17% on the final just to reach 50 overall.

Answer: You need 92% on the final for an 80 overall, and 17% on the final just to pass with 50 overall.

This assumes your 72% stays fixed as the 60% coursework part and that the final is worth exactly 40%; your course may add rules such as a minimum final mark or rounding.