Question

shaneka wharton has scores of 73, 81, 60, and 63 on her algebra tests.
use an inequality to find the score she must make on the final exam to pass the course with an average of 75 or higher, given that the final exam counts as two tests.
interpret the meaning of the answer in part (a).
the solution set is {x | \boxed{} } (type an inequality.)

Explanation:

Step1: Define variables and average formula

Let $x$ = final exam score. The final counts as 2 tests, so total "test equivalents" = $4 + 2 = 6$. The average inequality is:
$$\frac{73 + 64 + 82 + 83 + 2x}{6} \geq 75$$

Step2: Sum the known test scores

Calculate sum of existing scores:
$73 + 64 + 82 + 83 = 302$
Inequality becomes:
$$\frac{302 + 2x}{6} \geq 75$$

Step3: Eliminate denominator

Multiply both sides by 6:
$302 + 2x \geq 75 \times 6$
$302 + 2x \geq 450$

Step4: Isolate the variable term

Subtract 302 from both sides:
$2x \geq 450 - 302$
$2x \geq 148$

Step5: Solve for x

Divide both sides by 2:
$x \geq \frac{148}{2}$
$x \geq 74$

Answer:

a. $x \geq 74$
b. Shunika must score 74 or higher on her final exam (which counts as two test scores) to achieve an overall course average of 75 or higher.