Jackie scored 81 and 87 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 80 and 85, inclusive.
80 ≤ [(81 + 87 + x) / 3] ≤ 85
multiplying by 3 ... 240 ≤ (168 + x) ≤ 255
subtracting 168 ... 72 ≤ x ≤ 87
Thank you!
To find the possible values for a third quiz score, we need to calculate the average of the three quiz scores. Let's call the third quiz score "x".
The average of three numbers is found by adding them together and then dividing the sum by 3. So, the average of Jackie's quiz scores would be:
(81 + 87 + x) / 3
We want this average to be between 80 and 85, inclusive. In other words, it should be greater than or equal to 80 and less than or equal to 85.
Now, we can write a compound inequality to represent the range of possible values for the third quiz score:
80 ≤ (81 + 87 + x) / 3 ≤ 85
To solve this compound inequality, we can solve each part separately:
1. 80 ≤ (81 + 87 + x) / 3
Multiply both sides of the inequality by 3 to get rid of the fraction:
240 ≤ 81 + 87 + x
Combine like terms:
240 ≤ 168 + x
Subtract 168 from both sides:
72 ≤ x
2. (81 + 87 + x) / 3 ≤ 85
Multiply both sides of the inequality by 3:
81 + 87 + x ≤ 255
Combine like terms:
168 + x ≤ 255
Subtract 168 from both sides:
x ≤ 87
So, the compound inequality representing the range of possible values for the third quiz score is:
72 ≤ x ≤ 87
To find the possible values for a third quiz score that would give Jackie an average between 80 and 85 (inclusive), we need to find the range of values that the average can fall in.
Let's consider the average score of the three quizzes. We can set up the following compound inequality:
80 ≤ (81 + 87 + x) / 3 ≤ 85
Notice that we divide the sum of the scores by 3 because we have three quizzes.
To solve this compound inequality, we can multiply each part of the inequality by 3 to eliminate the fraction:
80 * 3 ≤ 81 + 87 + x ≤ 85 * 3
240 ≤ 168 + x ≤ 255
Next, we can subtract 168 from each part of the inequality, which will isolate the variable (x):
240 - 168 ≤ 168 + x - 168 ≤ 255 - 168
72 ≤ x ≤ 87
Therefore, the possible values for Jackie's third quiz score that would give her an average between 80 and 85, inclusive, are any scores between 72 and 87, inclusive.