5) On the past two quizzes, a student scored a 75 and 83. Write and solve a compound
inequality to find the possible values for the 3rd quiz score that would give her an average
between 85 and 90, inclusive.
average =
sum of all values
number of values
Let x be the score on the 3rd quiz.
The average score is given by (75 + 83 + x) / 3.
We want the average to be between 85 and 90, inclusive.
This can be written as the compound inequality:
85 ≤ (75 + 83 + x) / 3 ≤ 90
To solve this inequality, we can multiply all terms by 3 to eliminate the fraction:
255 ≤ 75 + 83 + x ≤ 270
Next, we can combine like terms:
255 ≤ 158 + x ≤ 270
Next, subtract 158 from all sides:
255 - 158 ≤ x ≤ 270 - 158
Simplifying:
97 ≤ x ≤ 112
So the possible values for the 3rd quiz score that would give her an average between 85 and 90, inclusive, are 97, 98, 99, ... , 110, 111, 112.