4) a student score is 83 and 91 on her first two quizzes. write and solve a compound inequality to find possible values for a thord quiz score that would give anverage between 85 and 90.
a. 85≤83+91+n/3 ≤90; 81≤n≤96
b. 85≤83+91/2+n≤90; -2≤n≤3
c. 90≤83+91+n/3 ≤85; 96≤n≤81
d. 83≤85+91+n/3 ≤90; 73≤n≤94
i don't understand this question
Too late but here you go answer is A I think
Average of three quizzes :
Av = ( 83 + 91 + n ) / 3
must be equal or greater of 85 and equal or less of 90
85 <= ( 83 + 91 + n ) / 3 <= 90
To solve this problem, we need to find the possible values for the third quiz score that would result in an average between 85 and 90.
Let's call the third quiz score "n".
To find the average, we add up all the scores and divide by the total number of quizzes. In this case, we have 3 quizzes. So, the average can be calculated as (83 + 91 + n) / 3.
To find the compound inequality, we want the average to be between 85 and 90. So, we can write the compound inequality as:
85 ≤ (83 + 91 + n) / 3 ≤ 90.
To solve this compound inequality, we can multiply all sides of the inequality by 3 to eliminate the fraction:
3 * 85 ≤ 3 * (83 + 91 + n) / 3 ≤ 3 * 90.
This simplifies to:
255 ≤ 83 + 91 + n ≤ 270.
Next, we can combine like terms:
255 ≤ 174 + n ≤ 270.
To isolate "n", we can subtract 174 from all sides of the inequality:
255 - 174 ≤ 174 + n - 174 ≤ 270 - 174.
This simplifies to:
81 ≤ n ≤ 96.
So, the compound inequality that represents the possible values for the third quiz score is 81 ≤ n ≤ 96.
Therefore, the correct answer is option a, which states: 85 ≤ 83 + 91 + n/3 ≤ 90; 81 ≤ n ≤ 96.