A student scored 78 and 92 on his first two quizzes. Use a compound inequality to find the possible values for a third quiz score that would give him an average between 80 and 85, inclusive. (1 point)
78<=x<=92
75<=x<=85***
70<=x<=85
80<=x<=85
80 <= (78+92+x)/3 <= 85
240 <= 170+x <= 255
70 <= x <= 85
Well, well, well, let's solve this puzzle with some humor!
Okay, my buddy, we have ourselves a student who scored a 78 and 92 on the first two quizzes. Now this student wants to get an average between 80 and 85.
To find the possible value for the third quiz score, we need to set up a compound inequality. So, listen carefully:
We want the average to be between 80 and 85, which means the sum of all three quiz scores divided by 3 has to be between 80 and 85. Got it?
Now, let's turn this into a compound inequality. What's the sum of the scores for the first two quizzes? It's 78 + 92, which gives us 170. Then, we'll plug in the values:
80 x 3 ≤ 170 + x ≤ 85 x 3
Now, let's simplify this. 80 times 3 is 240, and 85 times 3 is 255. So, our compound inequality becomes:
240 ≤ 170 + x ≤ 255
To get the possible values for the third quiz score, we need to isolate the 'x' in the middle. Subtracting 170 from each part gives us:
240 - 170 ≤ x ≤ 255 - 170
That simplifies to:
70 ≤ x ≤ 85
There you have it, my friend! The possible values for the third quiz score that would give our student an average between 80 and 85 are 70 to 85, inclusive. Keep aiming high, and remember, laughter is the best studying companion!
To find the possible values for a third quiz score that would give the student an average between 80 and 85, inclusive, we can use a compound inequality.
Let's denote the third quiz score as x.
The average of the three quiz scores can be calculated by finding the sum of the scores and dividing it by 3:
Average = (78 + 92 + x) / 3
We want this average to be between 80 and 85, inclusive:
80 ≤ (78 + 92 + x) / 3 ≤ 85
To simplify the inequality, we can multiply all parts by 3:
240 ≤ 78 + 92 + x ≤ 255
Combine the constant terms:
240 + 78 + 92 ≤ x ≤ 255 + 78 + 92
Simplify further:
410 ≤ x ≤ 425
So, the compound inequality that represents the possible values for the third quiz score is:
410 ≤ x ≤ 425
Therefore, the correct answer is:
75 ≤ x ≤ 85
To find the possible values for the third quiz score, we need to consider the average between 80 and 85, inclusive.
The average between 80 and 85 is (80 + 85) / 2 = 82.5.
We know that the student's score on the third quiz needs to give him an average between 80 and 85, inclusive. Therefore, the student's total score from the three quizzes should be between (80 + 85) / 2 = 82.5 and (85 + 85) / 2 = 85.
Let's represent the third quiz score as x. The compound inequality becomes:
82.5 <= (78 + 92 + x) / 3 <= 85
To simplify the compound inequality, we can multiply all the terms by 3:
247.5 <= 78 + 92 + x <= 255
Next, we can subtract 170 (combined value of 78 + 92):
77.5 <= x <= 85
Therefore, the correct compound inequality representing the possible values for the third quiz score is: 77.5 <= x <= 85.
So, from the given answer choices, the correct option is 75 <= x <= 85.