Question
A student scored 83 and 91 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive.
(1 point)
855. 83+91+n 3 90, 81n96
83+91 85≤ ≤ n, -2≤ n ≤3 2
90 ≤ 83 +91 + "<85,96 ≤ n ≤81 3
835 83+91+n 3 ≤90;73≤ n ≤94
(1 point)
855. 83+91+n 3 90, 81n96
83+91 85≤ ≤ n, -2≤ n ≤3 2
90 ≤ 83 +91 + "<85,96 ≤ n ≤81 3
835 83+91+n 3 ≤90;73≤ n ≤94
Answers
GPT 3.5
The compound inequality to find the possible values for a third quiz score, "n", is:
85 ≤ (83 + 91 + n)/3 ≤ 90
To solve this compound inequality:
1. Multiply all three parts of the compound inequality by 3 to eliminate the fraction:
255 ≤ (83 + 91 + n) ≤ 270
2. Simplify the inequality by combining like terms:
255 ≤ (174 + n) ≤ 270
3. Subtract 174 from each part of the inequality to isolate "n":
81 ≤ n ≤ 96
Therefore, the possible values for the third quiz score that would give her an average between 85 and 90, inclusive, are 81 ≤ n ≤ 96.
85 ≤ (83 + 91 + n)/3 ≤ 90
To solve this compound inequality:
1. Multiply all three parts of the compound inequality by 3 to eliminate the fraction:
255 ≤ (83 + 91 + n) ≤ 270
2. Simplify the inequality by combining like terms:
255 ≤ (174 + n) ≤ 270
3. Subtract 174 from each part of the inequality to isolate "n":
81 ≤ n ≤ 96
Therefore, the possible values for the third quiz score that would give her an average between 85 and 90, inclusive, are 81 ≤ n ≤ 96.