Solve the Weighted Average Puzzle: Determine the Missing Final Exam Grade

A teacher loses the final exam results of one of his students. Luckily for him, he had already calculated the student's average grade for this year.

AttendanceAssessmentAssignmentsFinal examGradeWeight10%10%20%60%958210060

If the student's average is 92, then what grade did he get on his final exam?

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1

Understand the problem

A teacher loses the final exam results of one of his students. Luckily for him, he had already calculated the student's average grade for this year.

AttendanceAssessmentAssignmentsFinal examGradeWeight10%10%20%60%958210060

If the student's average is 92, then what grade did he get on his final exam?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the weighted score for each component.
  • Step 2: Sum these scores and express the total weighted score needed for the average.
  • Step 3: Solve for the unknown final exam grade using the weighted average formula.

Now, let's work through each step:

Step 1: Calculate the individual components' weighted scores:

  • Attendance: 95×0.10=9.5 95 \times 0.10 = 9.5
  • Assessment: 82×0.10=8.2 82 \times 0.10 = 8.2
  • Assignments: 100×0.20=20.0 100 \times 0.20 = 20.0

Step 2: Calculate the total weighted score needed to achieve an average of 92.

The weighted average formula is given by:

Weighted Average=∑(Grade×Weight)=92 \text{Weighted Average} = \sum (\text{Grade} \times \text{Weight}) = 92 (9.5+8.2+20.0+Final Exam Grade×0.60)=92 (9.5 + 8.2 + 20.0 + \text{Final Exam Grade} \times 0.60) = 92

Simplifying what we know:

37.7+Final Exam Grade×0.60=92 37.7 + \text{Final Exam Grade} \times 0.60 = 92

Step 3: Solve for the final exam grade.

First, isolate the weighted exam score:

Final Exam Grade×0.60=92−37.7=54.3 \text{Final Exam Grade} \times 0.60 = 92 - 37.7 = 54.3

Next, solve for the actual final exam grade:

Final Exam Grade=54.30.60=90.5 \text{Final Exam Grade} = \frac{54.3}{0.60} = 90.5

Therefore, the grade the student received on the final exam is 90.5 90.5 .

3

Final Answer

90.5

Practice Quiz

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Norbert buys some new clothes.

When he gets home, he decides to work out how much each outfit cost him on average.

PriceOutfit4 T-shirts2 pairs of shorts3 pairs of pants2 sweaters45$50$80$100$210$1 coat

What answer should he come up with?

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