Math Problem Statement
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 is calculated as a weighted average:
The highest possible final exam score is 100%, so we substitute that into the formula:
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 in the same formula:
Simplify:
Subtract 62.25 from both sides:
Solve for the Final Exam Score:
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:
- What if the final exam accounted for 40% of the grade instead of 25%?
- How would the result change if the current average was 90%?
- What is the final score needed to achieve an overall grade of 85%?
- How would missing the final exam entirely affect the final grade?
- 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
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