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) Responses Image with alt text: 85 is less than or equal to 83 plus 91 plus n divided by 3 is less than or equal to 90; 81 is less than or equal to n is less than or equal to 96 Image with alt text: 85 is less than or equal to 83 plus 91 divided by 2 is less than or equal to n; negative 2 is less than or equal to n is less than or equal to 3 Image with alt text: 90 is less than or equal to 83 plus 91 plus n divided by 3 is less than or equal to 85; 96 is less than or equal to n is less than or equal to 81
The compound inequality to find the possible values for a third quiz score is:
85 ≤ (83 + 91 + n)/3 ≤ 90
To solve this inequality, we can multiply all sides of the inequality by 3 to remove the fraction:
255 ≤ 83 + 91 + n ≤ 270
Next, we can combine like terms:
255 ≤ 174 + n ≤ 270
Then, we can subtract 174 from all sides of the inequality:
255 - 174 ≤ n ≤ 270 - 174
81 ≤ n ≤ 96
Therefore, the possible values for a third quiz score that would give her an average between 85 and 90, inclusive, are 81 to 96.