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
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 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
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: 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
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
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
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
85 is less than or equal to 83 + 91 + n/3 is less than or equal to 90
Simplifying, we get:
255 is less than or equal to 174 + n is less than or equal to 270
Subtracting 174 from all parts of the inequality, we get:
81 is less than or equal to n is less than or equal to 96
Therefore, the possible values for the third quiz score, n, are between 81 and 96, inclusive.
To find the compound inequality for the third quiz score that would give her an average between 85 and 90, inclusive, we need to consider the average of all three scores (First Quiz + Second Quiz + Third Quiz divided by 3) being between 85 and 90 (inclusive).
Let's break down the problem step by step:
Step 1: Calculate the average of the first two quiz scores:
Average = (First Quiz + Second Quiz) / 2
Average = (83 + 91) / 2
Average = 174 / 2
Average = 87
Step 2: Set up the compound inequality using the average as the middle value:
85 ≤ (83 + 91 + Third Quiz) / 3 ≤ 90
Step 3: Simplify the compound inequality:
85 ≤ (174 + Third Quiz) / 3 ≤ 90
Step 4: Multiply both sides of the inequality by 3 to eliminate the denominator:
255 ≤ 174 + Third Quiz ≤ 270
Step 5: Subtract 174 from all parts of the inequality:
255 - 174 ≤ Third Quiz ≤ 270 - 174
81 ≤ Third Quiz ≤ 96
Therefore, the compound inequality for the possible values of the third quiz score is:
81 ≤ Third Quiz ≤ 96.
The correct compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive is:
85 ≤ (83 + 91 + n)/3 ≤ 90
To solve this inequality, we can first simplify it:
83 + 91 + n ≤ 3(90)
174 + n ≤ 270
n ≤ 270 - 174
n ≤ 96
Now, we can find the lower value:
83 + 91 + n ≥ 3(85)
174 + n ≥ 255
n ≥ 255 - 174
n ≥ 81
Therefore, the solution to the compound inequality is 81 ≤ n ≤ 96.
So, the possible values for a third quiz score to get an average between 85 and 90, inclusive, are any numbers from 81 to 96.