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A social studies teacher weighs scores on tests at 50 percent, homework at 30 percent, and class participation at 20 percent.

Which student will receive the highest grade based on this grading system?

Sophia gets 75 percent on tests, completes all of her homework, and attends half of the classes.
Maya gets an 88 percent on tests, completes all of her homework, and sometimes participates in class.
Amit gets a 65 percent on tests, completes all of his homework, and participates in class regularly.
Elias gets a 97 percent on tests, does all of his homework, and participates in class regularly.

1 answer

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%.