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
1. 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
2. 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
3. 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
4. 83 is less than or equal to 83 plus 91 plus n divided by 3 is less than or equal to 90; 73 is less than or equal to n is less than or equal to 94
The correct compound inequality is:
85 ≤ (83 + 91 + n)/3 ≤ 90
To solve this compound inequality, we can start by multiplying every term by 3 to get rid of the denominator:
255 ≤ 83 + 91 + n ≤ 270
Next, we combine like terms:
255 ≤ 174 + n ≤ 270
Subtract 174 from all terms:
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.
So, the correct answer is:
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. (Option 1)