To find the minimum grade needed on the final exam to achieve an overall grade of 83% in the class, we can set up the equation using the weights of each category.
Step 1: Convert the weights to decimals
- Attendance: 10% = 0.10
- Tests: 30% = 0.30
- Homework: 20% = 0.20
- Final Exam: 40% = 0.40
Step 2: Set up the equation
Let \( x \) be the grade needed on the final exam. The overall grade can be calculated using the formula:
\[ \text{Overall Grade} = (\text{Attendance Grade} \times \text{Weight}) + (\text{Test Grade} \times \text{Weight}) + (\text{Homework Grade} \times \text{Weight}) + (x \times \text{Weight}) \]
Substituting the known values into the equation:
\[ 0.10 \times 100 + 0.30 \times 80 + 0.20 \times 95 + 0.40 \times x = 83 \]
Step 3: Calculate the contributions of each category
- Attendance contribution: \( 0.10 \times 100 = 10 \)
- Tests contribution: \( 0.30 \times 80 = 24 \)
- Homework contribution: \( 0.20 \times 95 = 19 \)
Step 4: Combine the contributions and solve for \( x \)
Now plug these values back into the equation:
\[ 10 + 24 + 19 + 0.40x = 83 \]
Combine the known contributions:
\[ 53 + 0.40x = 83 \]
Subtract 53 from both sides:
\[ 0.40x = 30 \]
Step 5: Solve for \( x \)
Now, divide both sides by 0.40:
\[ x = \frac{30}{0.40} = 75 \]
Conclusion
The minimum grade needed on the final exam to earn an overall grade of 83% in the class is 75%. Thus, the answer is:
75%
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