Answer:
[tex] 85 \le \frac{75 + 97 + n}{3} \le 90 [/tex]; [tex] 83 \le n \le 98 [/tex]
Step-by-step explanation:
Score of the first two quizzes: 75 and 97
Let n represent the third score
Average score would be: [tex] \frac{75 + 97 + n}{3} [/tex].
Given that the average score fall between 85 and 90, this can be represented by the compound inequality as shown below:
[tex] 85 \le \frac{75 + 97 + n}{3} \le 90 [/tex]
Solve for n in each statement that makes up the compound inequality:
[tex] 85 \le \frac{75 + 97 + n}{3} [/tex]
[tex] 85 \le \frac{172 + n}{3} [/tex]
Multiply both sides by 3
[tex] 85*3 \le 172 + n [/tex]
[tex] 255 \le 172 + n [/tex]
Subtract 172 from each side of the inequality
[tex] 255 - 172 \le n [/tex]
[tex] 83 \le n [/tex]
Also,
[tex] \frac{75 + 97 + n}{3} \le 90 [/tex]
[tex] \frac{172 + n}{3} \le 90 [/tex]
Multiply both sides by 3
[tex] 172 + n \le 90*3 [/tex]
[tex] 172 + n \le 270 [/tex]
Subtract 172 from both sides of the inequality
[tex] n \le 270 - 172 [/tex]
[tex] n \le 98 [/tex]
Combining both together, the possible values of her third quiz score would be:
[tex] 83 \le n \le 98 [/tex]
