Question

susie washington has scores of 61, 64, 77, and 86 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 73 or higher, given that the final exam counts as two tests. b. explain the meaning of the answer to part (a). a. the solution set is {x| } (type an inequality.)

Explanation:

Step1: Calculate the sum of the known scores

The known scores are 61, 64, 77, 86. The sum $S = 61+64 + 77+86=288$.

Step2: Set up the average - score inequality

Let the score on the final exam be $x$. Since the final exam counts as two tests, the total number of "test - equivalents" is $4 + 2=6$. The average score $\bar{A}=\frac{288 + 2x}{6}$. We want $\bar{A}\geq73$. So, $\frac{288+2x}{6}\geq73$.

Step3: Solve the inequality for $x$

Multiply both sides of the inequality $\frac{288 + 2x}{6}\geq73$ by 6: $288+2x\geq73\times6$.
$288+2x\geq438$.
Subtract 288 from both sides: $2x\geq438 - 288$.
$2x\geq150$.
Divide both sides by 2: $x\geq75$.

Answer:

$\{x|x\geq75\}$