What grade do I need to make on my final exam in order to have a test average of 75?

[匿名]

2019-12-04 6:39 pm

The exams count for 70% of the entire grade. However, I am only worried about the exam score, as the remaining 30% will only boost my grade. I need that 70% to be converted into 100% in order to find out what I need on my final exam. The first exam is worth 12% of my grade, and I made a 78.72 on it. The second test is worth 12% of my grade, and I made a 69.16 on it. The third test is worth 10% of my grade, and I made an 84% on it. The fourth test is worth 10%, and I made an 88 on it. The 5th test is worth 10%, and I made an 82 on it. What do I need on the 6th exam, which is worth 16% of my grade? I worked it out and got a 59. Please let me know if this is correct.

回答 (1)

Puzzling

2019-12-04 7:16 pm

Take a weighted average. You want that to be at least 75. Since the tests account for 70% and you are ignoring the other 30%, multiply each by their weight and divide by 70% (0.70).

Weighted average is at least 75%:
[(0.12 * 78.72) + (0.12 * 69.16) + (0.10 * 84) + (0.10 * 88) + (0.10 * 82) + (0.16 * x)] / 0.70 ≥ 75

Multiply both sides by 0.70;
(0.12 * 78.72) + (0.12 * 69.16) + (0.10 * 84) + (0.10 * 88) + (0.10 * 82) + (0.16 * x) ≥ 52.5

Multiply out the rest:
9.4464 + 8.2992 + 8.4 + 8.8 + 8.2 + 0.16x ≥ 52.5

Add:
43.1456 + 0.16x ≥ 52.5

Subtract 43.1456 from both sides:
0.16x ≥ 52.5 - 43.1456
0.16x ≥ 9.3544

Divide both sides by 0.16:
x ≥ 9.3544 / 0.16
x ≥ 58.465

Answer:
Assuming you have at least a 75% on the other work, you just need to get at least 58.465 on the final test.

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