Calculating a Weighted Average

The following table demonstrates how a weighted grade is calculated. The percentage in each category is multiplied by its respective weight. The sum of the results is the total grade percentage.

CategoryPercentage in Category Weight of CategoryResult
Homework 93% x .30 0.279
Quiz/Test 88% x .50 0.440
Exam 91% x .20 0.182
  .901
Total 90.1%

The question that often arises is "What must I get on the final to bring my grade to a certain level?" Let us represent the above table as an algebraic expression using hq, ande to represent the categories: homework, quiz/test, and exam respectively. This is done as follows: h*the weight of h + q*the weight of q + e*the weight of e = final grade. To solve for the grade on the exam, enter in the available information with x representing the grade on the final exam and the desired grade for the class. The following is an example.

CategoryPercentage in Category Weight of CategoryResult
Homework 95% x .30 0.285
Quiz/Test 86% x .50 0.43
Exam ? x .20 ?
Total 90%

Mathematically this problem can then be solved as follows.

h*(the weight of h) + q*(the weight of q) + e*(the weight of e) = final grade
(.95)*(.30) + (.86)*(.50) + x (.20) = .90
.285 + .43 + .2x = .90
.715 + .2x = .90
.2x = .90 - .715
.2x = .185
x = .185/.2
x = .925
92.5%

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