a student scores 76,82,83 on the first three test, she has a 92 homework averge. if the final exam is 50% of grade and homework is 10% and the test average (nit including the final) is 40% then what grade should she get on the final exam to get a 87.5 in the class?
Let her grade on the final be x
.5x + .1(92) + .4(76+82+83)/3 = 87.5
solve for x
(I get 92.3)
To determine the required grade on the final exam, we need to consider the weightage of each component of the final grade and calculate the average grade needed. Let's break down the calculation:
1. Test Average: Since the final exam is not included in the test average, we only consider the scores from the first three tests. The average test score is given by:
`(76 + 82 + 83) / 3 = 80.33`
2. Homework Average: The homework average is given as 92.
3. Final Exam Weightage: The final exam contributes 50% to the final grade.
4. Homework Weightage: The homework contributes 10% to the final grade.
5. Test Average Weightage: The test average contributes 40% to the final grade.
Now, let's set up the equation to find the required grade on the final exam (F):
0.10 * 92 + 0.40 * 80.33 + 0.50 * F = 87.5
Simplifying the equation:
9.2 + 32.132 + 0.50F = 87.5
Combining like terms:
41.332 + 0.50F = 87.5
Subtracting 41.332 from both sides:
0.50F = 46.168
Dividing by 0.50:
F = 92.336
Therefore, she would need to score approximately 92.336 on the final exam to obtain a final grade of 87.5 in the class.