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
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.
To find the possible values for the third quiz score that would give the student an average between 85 and 90, inclusive, we can set up a compound inequality.
Let n represent the third quiz score.
The first quiz score is 83, and the second quiz score is 91.
The average is given by the formula: Average = (First Score + Second Score + Third Score) / 3
Setting up the inequality:
85 ≤ (83 + 91 + n) / 3 ≤ 90
To simplify the inequality, multiply both sides by 3:
255 ≤ 83 + 91 + n ≤ 270
Combine like terms:
255 ≤ 174 + n ≤ 270
Subtract 174 from all sides:
81 ≤ n ≤ 96
Therefore, the possible values for the third quiz score, n, are between 81 and 96, inclusive.
To solve this problem, we need to find the range of possible values for the third quiz score that would give the student an average between 85 and 90, inclusive.
Let's represent the third quiz score by the variable "n".
The average of the three quiz scores can be calculated by adding all three scores and dividing by 3. So, the average is (83 + 91 + n) / 3.
To find the range of possible values for "n", we need to write a compound inequality that represents the average being between 85 and 90, inclusive.
The compound inequality can be written as:
85 ≤ (83 + 91 + n) / 3 ≤ 90
To solve this compound inequality, we can multiply all the terms in the inequality by 3 to eliminate the fraction:
255 ≤ 83 + 91 + n ≤ 270
Next, we can combine the constant terms:
255 + 83 + 91 ≤ n ≤ 270 + 83 + 91
Simplifying, we have:
429 ≤ n ≤ 444
Therefore, the possible values for the third quiz score "n" that would give the student an average between 85 and 90, inclusive, are 429 ≤ n ≤ 444.