Question

marilee wants to earn an \a\ in a class and needs an overall average of at least 91. her test grades are 100, 99, 100, and 97. the average of her quizzes is 90. the final exam counts as 2 test grades. what scores on the final exam would result in marilees overall average of 91 or greater? marilee must earn a score of select > to earn an \a\ in the class.

Explanation:

Step1: Calculate the sum of the 4 non - final - exam test grades

The 4 test grades are 91, 100, 99, 100. The sum $S_1=91 + 100+99 + 100=390$.

Step2: Let the final - exam score be $x$.

The final - exam counts as 2 test grades. So the total number of "test - grade equivalents" is $4 + 2=6$.

Step3: Set up the inequality for the overall average.

The average of all the grades (including the final - exam) should be at least 91. The formula for the average $\bar{A}=\frac{S_1 + 2x}{6}\geq91$.

Step4: Solve the inequality for $x$.

First, multiply both sides of the inequality $\frac{390+2x}{6}\geq91$ by 6: $390 + 2x\geq91\times6$.
$390+2x\geq546$.
Then subtract 390 from both sides: $2x\geq546 - 390$.
$2x\geq156$.
Divide both sides by 2: $x\geq78$.

Answer:

78