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.
A. 85 ≤ 83+91+n/3 ≤ 90, 81≤ n ≤ 96
B. 83+91 85≤ ≤ n, -2≤ n ≤3 2
C. 90 ≤ 83 +91 + "<85,96 ≤ n ≤81 3
D.835 83+91+n 3 ≤90;73≤ n ≤94
A. 85 ≤ (83 + 91 + n)/3 ≤ 90, 81 ≤ n ≤ 96
To find the possible values for the third quiz score, we need to determine the average score. The average score is found by dividing the sum of the scores by the number of quizzes. In this case, the sum of the scores is 83 + 91 + n, and the number of quizzes is 3.
To calculate the average score, we divide the sum of the scores by 3:
(83 + 91 + n)/3
To ensure that the average score is between 85 and 90 (inclusive), we set up the compound inequality:
85 ≤ (83 + 91 + n)/3 ≤ 90
By solving this compound inequality, we find that the possible values for the third quiz score, n, are between 81 and 96 (inclusive).
Answer: A. 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's define the third quiz score as "n".
The average of the three quiz scores can be found by summing the three scores and dividing by 3. So we have:
(83 + 91 + n)/3
We want this average to be between 85 and 90, inclusive. Therefore, the compound inequality is:
85 ≤ (83 + 91 + n)/3 ≤ 90
To simplify this compound inequality, we can multiply each term by 3:
85*3 ≤ 83 + 91 + n ≤ 90*3
255 ≤ 83 + 91 + n ≤ 270
Now, we can subtract 83 + 91 from all three parts of the compound inequality:
255 - 83 - 91 ≤ 83 + 91 + n - 83 - 91 ≤ 270 - 83 - 91
81 ≤ n ≤ 96
So, the compound inequality that represents the possible values for the third quiz score is:
A. 85 ≤ 83+91+n/3 ≤ 90, 81≤ n ≤ 96
To find the compound inequality to determine the possible values for the third quiz score, we need to consider the average between 85 and 90, inclusive.
First, we find the total score of the first two quizzes. The student scored 83 and 91, so the total is 83 + 91 = 174.
Next, we need to determine the range of possible values for the third quiz score, denoted as 'n', that would give an average between 85 and 90, inclusive.
To calculate the average, we divide the total score by the number of quizzes: (83 + 91 + n) / 3.
The compound inequality for the average score between 85 and 90, inclusive, would be: 85 ≤ (83 + 91 + n) / 3 ≤ 90.
Let's simplify this compound inequality:
Multiply each part by 3 to remove the fraction: (85 * 3) ≤ 83 + 91 + n ≤ (90 * 3).
This simplifies to: 255 ≤ 174 + n ≤ 270.
To isolate the variable 'n', we subtract 174 from each part: 255 - 174 ≤ n ≤ 270 - 174.
Simplifying further, 81 ≤ n ≤ 96.
Therefore, option A is the correct compound inequality:
85 ≤ (83 + 91 + n) / 3 ≤ 90, 81 ≤ n ≤ 96.