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.
To find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive, we need to set up a compound inequality.
Let's represent the third quiz score as x.
The average of the 3 quiz scores can be calculated by summing up the scores and dividing by 3:
(83 + 91 + x) / 3
We want this average to be between 85 and 90, inclusive. So the compound inequality is:
85 ≤ (83 + 91 + x) / 3 ≤ 90
To solve this compound inequality, we can multiply each term by 3:
255 ≤ 83 + 91 + x ≤ 270
Next, we can simplify the expression:
255 ≤ 174 + x ≤ 270
Then, we can subtract 174 from each term:
255 - 174 ≤ x ≤ 270 - 174
81 ≤ x ≤ 96
Therefore, the possible values for a third quiz score that would give her an average between 85 and 90, inclusive, are between 81 and 96, inclusive.
To solve this problem, we can start by finding the range of possible averages. The average score can be found by dividing the sum of all three quiz scores by 3.
Let's denote the score on the third quiz as "x". The sum of the first two quiz scores is 83 + 91 = 174.
So, the average score can be calculated as (174 + x) / 3.
We want the average to be between 85 and 90, inclusive. Therefore, the compound inequality for the average would be:
85 ≤ (174 + x) / 3 ≤ 90
To solve this compound inequality, we can start by multiplying all parts of the inequality by 3 to eliminate the denominator:
255 ≤ 174 + x ≤ 270
Next, subtract 174 from all parts of the inequality:
255 - 174 ≤ x ≤ 270 - 174
Simplifying, we get:
81 ≤ x ≤ 96
Therefore, the possible values for the third quiz score, x, that would give the student an average between 85 and 90, inclusive, are between 81 and 96.
To find the possible values for the third quiz score, we need to determine the range of values that would give the student an average between 85 and 90, inclusive.
Let's assume the third quiz score is represented by the variable x.
We know that the average score is calculated by summing all the scores and dividing by the number of quizzes. In this case, the average score is represented by the expression: (83 + 91 + x)/3.
To find the compound inequality, we can set up the following inequality based on the given conditions:
85 ≤ (83 + 91 + x)/3 ≤ 90
To solve this compound inequality, we can start by multiplying both sides of the inequality by 3 to eliminate the denominator:
255 ≤ 83 + 91 + x ≤ 270
Next, simplify the inequality:
255 ≤ 174 + x ≤ 270
Now, subtract 174 from each part of the inequality:
255 - 174 ≤ 174 + x - 174 ≤ 270 - 174
81 ≤ x ≤ 96
Therefore, the possible values for the third quiz score, x, are between 81 and 96, inclusive.