Question

trent earns scores of 70, 80, and 72 on three chapter tests for a certain class. his homework grade is 64 and his grade for a class project is 69. the overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the grade; the project accounts for 20%; and the final exam accounts for 20%. what scores can trent earn on the final exam to pass the course if he needs a \c\ or better? a \c\ or better requires an overall score of 70 or better, and 100 is the highest score that can be earned on the final exam. assume that only whole - number scores are given.
to obtain a \c\ or better, trent needs to score between □ and □, inclusive.

Explanation:

Step1: Calculate average of chapter tests

The average of the three chapter - tests with scores 70, 80, and 72 is $\frac{70 + 80+72}{3}=\frac{222}{3}=74$.

Step2: Set up the weighted - average equation

Let $x$ be the score on the final exam. The weighted - average formula for the course grade $G$ is $G = 0.5\times74+0.1\times64 + 0.2\times69+0.2x$.

Step3: Simplify the non - final - exam part of the equation

$0.5\times74 = 37$, $0.1\times64 = 6.4$, and $0.2\times69 = 13.8$. So the equation becomes $G=37 + 6.4+13.8+0.2x=57.2 + 0.2x$.

Step4: Solve for the minimum value of $x$

Since a "C" or better requires $G\geq70$, we set up the inequality $57.2+0.2x\geq70$. Subtract 57.2 from both sides: $0.2x\geq70 - 57.2=12.8$. Then divide both sides by 0.2: $x\geq\frac{12.8}{0.2}=64$.

Step5: Consider the maximum value of $x$

The maximum score on the final exam is 100.

Answer:

64 and 100