Question

shanika westborn has scores of 87, 87, 80, and 64 on her algebra tests.
a. (use an inequality to find the scores she must make on the final exam to pass the course with an average of 77 or higher, given that the final exam counts as two tests.
b. explain the meaning of the answer to part (a)

1. the solution set is \\(\\{x\\ \square\\}\\) (type an inequality)

Explanation:

Step1: Define total test equivalents

Let $x$ = final exam score. Final counts as 2 tests, so total test equivalents = $4 + 2 = 6$.

Step2: Set up average inequality

Average ≥ 77, so $\frac{87 + 87 + 80 + 64 + 2x}{6} \geq 77$

Step3: Sum existing scores

Calculate sum: $87+87+80+64 = 318$

Step4: Simplify the inequality

Substitute sum: $\frac{318 + 2x}{6} \geq 77$
Multiply both sides by 6: $318 + 2x \geq 77 \times 6$
$318 + 2x \geq 462$

Step5: Solve for x

Subtract 318: $2x \geq 462 - 318$
$2x \geq 144$
Divide by 2: $x \geq 72$

Answer:

a. $\{x \mid x \geq 72\}$
b. This means Shireika must score 72 or higher on her final exam (which is weighted like two regular tests) to achieve an overall course average of at least 77 and pass the course.