To determine which student receives the highest grade based on the grading system, we can calculate each student's overall score using the weights provided: tests (50%), homework (30%), and class participation (20%).
Let's calculate each student's score step by step.
1. Sophia:
- Test Score: 75%
- Homework Score: 100% (completes all homework)
- Class Participation Score: 50% (attends half the classes)
Calculating the weighted score: \[ \text{Overall Score} = (0.5 \times 75) + (0.3 \times 100) + (0.2 \times 50) \] \[ = 37.5 + 30 + 10 = 77.5% \]
2. Maya:
- Test Score: 88%
- Homework Score: 100% (completes all homework)
- Class Participation Score: Let's assume "sometimes participates" is around 60% (this is an estimation as it is not provided).
Calculating the weighted score: \[ \text{Overall Score} = (0.5 \times 88) + (0.3 \times 100) + (0.2 \times 60) \] \[ = 44 + 30 + 12 = 86% \]
3. Amit:
- Test Score: 65%
- Homework Score: 100% (completes all homework)
- Class Participation Score: 100% (participates regularly)
Calculating the weighted score: \[ \text{Overall Score} = (0.5 \times 65) + (0.3 \times 100) + (0.2 \times 100) \] \[ = 32.5 + 30 + 20 = 82.5% \]
4. Elias:
- Test Score: 97%
- Homework Score: 100% (does all homework)
- Class Participation Score: 100% (participates regularly)
Calculating the weighted score: \[ \text{Overall Score} = (0.5 \times 97) + (0.3 \times 100) + (0.2 \times 100) \] \[ = 48.5 + 30 + 20 = 98.5% \]
Summary of Scores:
- Sophia: 77.5%
- Maya: 86%
- Amit: 82.5%
- Elias: 98.5%
Conclusion: Elias receives the highest grade with an overall score of 98.5%.