A student scored 84 and 90 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
90, inclusive.
Well, scoring quizzes is serious business, but let's add a little fun to it!
Let's call the third quiz score "x" (not to be confused with Professor X from the X-Men).
To find the average between 80 and 90, inclusive, we need to write a compound inequality. The average of three quizzes can be found by adding the scores and dividing by 3:
(84 + 90 + x) / 3
We want this average to be between 80 and 90, so we can write the compound inequality:
80 ≤ (84 + 90 + x) / 3 ≤ 90
To solve this compound inequality, let's simplify it a bit. First, multiply both sides by 3 to get rid of the fraction:
240 ≤ 84 + 90 + x ≤ 270
Now, let's combine like terms:
240 ≤ 174 + x ≤ 270
Next, let's get rid of the 174 by subtracting it from all sides:
240 - 174 ≤ 174 + x - 174 ≤ 270 - 174
This simplifies to:
66 ≤ x ≤ 96
So, the possible values for the third quiz score that would give the student an average between 80 and 90 (inclusive) are between 66 and 96. Keep up the good work and try to score closer to 96, but remember to have fun while doing it!
To find the possible values for the third quiz score, let's represent the average as a compound inequality:
Given that the student scored 84 and 90 on her first two quizzes, let's denote the score on the third quiz as "x".
To find the average, we sum up the scores and divide by the total number of quizzes, which in this case is 3.
The equation for the average score is:
(84 + 90 + x) / 3
To find the compound inequality, we need to ensure that the average score is between 80 and 90, inclusive:
80 ≤ (84 + 90 + x) / 3 ≤ 90
Now we can solve this compound inequality step-by-step.
Step 1: Multiply all parts of the compound inequality by 3 to eliminate the fraction:
3*80 ≤ 3*((84 + 90 + x) / 3) ≤ 3*90
240 ≤ 84 + 90 + x ≤ 270
Step 2: Simplify the inequality:
240 + 84 + 90 ≤ 84 + 90 + x ≤ 270 + 84 + 90
414 ≤ 174 + x ≤ 444
Step 3: Subtract 174 from all parts of the inequality:
414 - 174 ≤ 174 + x - 174 ≤ 444 - 174
240 ≤ x ≤ 270
Therefore, the possible values for the third quiz score that would give her an average between 80 and 90, inclusive, are between 240 and 270.
To find the possible values for the third quiz score that would give her an average between 80 and 90, inclusive, we can use a compound inequality.
Let's assume the third quiz score as 'x'.
The average can be calculated by summing up all the quiz scores and dividing by the number of quizzes taken.
We know that the student scored 84 and 90 on her first two quizzes. So, the sum of the first two scores would be 84 + 90 = 174.
To find the possible values for the third quiz score, we need to find the range of 'x' that would give us an average between 80 and 90, inclusive.
The average score can be calculated by dividing the sum of the three quiz scores by 3, which must be within the range of 80 and 90, inclusive.
Therefore, the compound inequality for the possible values of 'x' would be:
(174 + x)/3 ≥ 80 and (174 + x)/3 ≤ 90
Now, we need to solve this compound inequality to find the range of values for 'x'.
Multiplying the entire compound inequality by 3 to eliminate the fraction, we get:
174 + x ≥ 240 and 174 + x ≤ 270
Subtracting 174 from both sides, we have:
x ≥ 66 and x ≤ 96
Thus, the possible values for the third quiz score that would give her an average between 80 and 90, inclusive, are between 66 and 96, inclusive.
80 < (84+90+x)/3 < 90
240 < 174+x < 270
66 < x < 96