Robert knows from reading his syllabus in intermediate...

Robert knows from reading his syllabus in intermediate algebra that the average of his chapter tests accounts for $60 \%$ ( 0.6 ) of his overall course grade. He also knows that the final exam counts as $40 \%$ (0.4) of his grade. a. Suppose that the average of Robert's chapter tests is $89 \%$. Determine the range of grades that he would need on his final exam to get an "A" in the class. (Assume that a grade of "A" is obtained if Robert's overall average is $90 \%$ or better.) b. Determine the range of grades that Robert would need on his final exam to get a "B" in the class. (Assume that a grade of "B" is obtained if Robert's overall average is at least $80 \%$ but less than $90 \%$.)

Robert knows from reading his syllabus in intermediate algebra that the average of his chapter tests accounts for $60 \%$ ( 0.6 ) of his overall course grade. He also knows that the final exam counts as $40 \%$ (0.4)
of his grade.
a. Suppose that the average of Robert's chapter tests is $89 \%$. Determine the range of grades that he would need on his final exam to get an "A" in the class. (Assume that a grade of "A" is obtained if Robert's overall average is $90 \%$ or better.)
b. Determine the range of grades that Robert would need on his final exam to get a "B" in the class. (Assume that a grade of "B" is obtained if Robert's overall average is at least $80 \%$ but less than $90 \%$.)

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Key Concepts

Linear Equations and Inequalities

Solving linear equations and inequalities involves isolating the unknown variable by performing algebraic operations. When determining required scores on an exam given a target overall grade, the problem is usually expressed as a linear equation or inequality that incorporates weights and known scores, and solving it provides the range of acceptable scores.

Percentages

Percentages represent parts per hundred and are commonly used in grading systems to express performance levels. Understanding percentages is crucial for converting raw scores or averages into a standardized form, which can then be manipulated within weighted averages or compared against grade thresholds.

Weighted Averages

Weighted averages are used to compute an overall score by multiplying each component by its respective weight and then summing the results. In academic grading, different assessments can contribute unequally to the final grade, so the weighted average combines these scores proportionally to reflect their importance in the overall evaluation.

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