Question

shereka washburn 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).

c. the solution set is \\{x | \boxed{} \\} (type an inequality)

Explanation:

Step1: Define variables and average formula

Let $x$ = final exam score. Since the final counts as 2 tests, total "test equivalents" = $4 + 2 = 6$. The average inequality is:
$$\frac{87 + 87 + 80 + 64 + 2x}{6} \geq 77$$

Step2: Sum the known test scores

Calculate the sum of existing scores:
$$87 + 87 + 80 + 64 = 318$$

Step3: Simplify the inequality

Substitute the sum and multiply both sides by 6:
$$318 + 2x \geq 77 \times 6$$
$$318 + 2x \geq 462$$

Step4: Isolate the term with $x$

Subtract 318 from both sides:
$$2x \geq 462 - 318$$
$$2x \geq 144$$

Step5: Solve for $x$

Divide both sides by 2:
$$x \geq 72$$

Answer:

a. The solution set is $\{x \mid x \geq 72\}$
b. The inequality result means Shureika must score 72 or higher on her final exam (which counts as two test scores) to have an overall course average of at least 77 and pass the course.