Maria wants to achieve an overall average of 85% in her university course. The final exam for the course is worth 40% of her overall grade, while her assignments (60% of her grade) have an average of 82%. What grade does Maria need on her final exam to reach her desired average?(A:1)

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BlackTom AI · Accepted Answer

We’re told Maria wants an overall average of 85% and the grading weights are: final exam = 40%, assignments = 60% with an average of 82%. 
First, compute the contribution from assignments: 0.60 * 82 = 49.2 points toward the overall grade. 
Next, let x be the final exam score (as a percentage). The final exam contributes 0.40 * x to the overall grade. The total must equal 85, so:
0.40 * x + 49.2 = 85.
Subtract 49.2 from both sides: 0.40 * x = 35.8.
Divide both sides by 0.40: x = 35.8 / 0.40 = 89.5.
Now, examine each option:
- Option a: 88% would give total = 0.40*88 + 49.2 = 35.2 + 49.2 = 84.4. This is below the target 85, so this option does not meet the goal and is incorrect.
- Option b: 35.7% is far too low for a final exam score in this context; its contribution would be 0.40*35.7 = 14.28, and total would be 14.28 + 49.2 = 63.48, which is far from 85. This is incorrect.
- Option c: 89.5% yields total = 0.40*89.5 + 49.2 = 35.8 + 49.2 = 85.0, exactly meeting the desired average. This aligns with the calculation and is the correct mathematical target.
- Option d: 80% gives 0.40*80 = 32, so total = 32 + 49.2 = 81.2, which is below 85, making this incorrect.

In summary, the required final exam grade to achieve an 85% overall is 89.5%. The option resembling this value (if present) would be the correct one, while the other choices fail to reach the target because they under- or mis-estimate the final exam’s impact on the overall average.

Maria wants to achieve an overall average of 85% in her university course. The final exam for the course is worth 40% of her overall grade, while her assignments (60% of her grade) have an average of 82%. What grade does Maria need on her final exam to reach her desired average?(A:1)

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