Math Problem Statement

A friend has an 83% average before the final exam for a course. That score includes everything but the final, which counts for 25% of the course grade. What is the best course grade your friend can earn? What is the minimum score your friend would need on the final to earn a 75% for the course?

Solution

Let's break down and solve the problem from your screenshot.

Problem 1: Best course grade your friend can earn

  • Given:
    • Current average: 83%
    • The final exam counts for 25% of the course grade.

The course grade GG is calculated as a weighted average:

G=(0.75×83)+(0.25×Final Exam Score)G = (0.75 \times 83) + (0.25 \times \text{Final Exam Score})

The highest possible final exam score is 100%, so we substitute that into the formula:

G=(0.75×83)+(0.25×100)G = (0.75 \times 83) + (0.25 \times 100)

G=62.25+25=87.25G = 62.25 + 25 = 87.25

So, the best course grade your friend can earn is 87.3% (rounded to one decimal place).

Problem 2: Minimum score on the final to earn a 75% overall

We need to determine the minimum final exam score needed to achieve a 75% course grade. Set G=75G = 75 in the same formula:

75=(0.75×83)+(0.25×Final Exam Score)75 = (0.75 \times 83) + (0.25 \times \text{Final Exam Score})

Simplify:

75=62.25+0.25×Final Exam Score75 = 62.25 + 0.25 \times \text{Final Exam Score}

Subtract 62.25 from both sides:

12.75=0.25×Final Exam Score12.75 = 0.25 \times \text{Final Exam Score}

Solve for the Final Exam Score:

Final Exam Score=12.750.25=51\text{Final Exam Score} = \frac{12.75}{0.25} = 51

So, your friend needs a minimum score of 51% on the final to earn a 75% overall grade.


Would you like more details or have any questions?

Here are 5 related questions to expand on this:

  1. What if the final exam accounted for 40% of the grade instead of 25%?
  2. How would the result change if the current average was 90%?
  3. What is the final score needed to achieve an overall grade of 85%?
  4. How would missing the final exam entirely affect the final grade?
  5. Can your friend achieve a 90% overall grade, and what score would be needed?

Tip: Always double-check that you're using the correct percentage weighting for different grade components when calculating final grades!

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Math Problem Analysis

Mathematical Concepts

Weighted Average
Algebra
Percentage Calculations

Formulas

Course Grade (G) = (0.75 × Current Average) + (0.25 × Final Exam Score)
To find the Final Exam Score needed for a target grade, solve: G = (0.75 × Current Average) + (0.25 × Final Exam Score)

Theorems

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Suitable Grade Level

Grades 9-12