I'm not sure how to do this. Can anyone help me solve it correctly?
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 get her an average between 85 and 90, inclusive.
the total points for the 3 tests is 3 times the average, so we need
3*85 <= 75+83+x <= 3*90
255 <= 158+x <= 270
97 <= x <= 112
So, only a 97,98,99 or 100 will raise her average that much.
Ok I got 91<=x<=101
Is this correct?
Thank you Steve!
To find the possible values for the 3rd quiz score, we need to set up a compound inequality. First, let's calculate the average of the past two quizzes:
Average = (75 + 83) / 2 = 158 / 2 = 79
Now, we want the average of the three quizzes to be between 85 and 90, inclusive. We can set up the following compound inequality:
85 ≤ (75 + 83 + x) / 3 ≤ 90
To solve this inequality, we can multiply each part of the inequality by 3 to get rid of the fraction:
85*3 ≤ 75 + 83 + x ≤ 90*3
255 ≤ 158 + x ≤ 270
Next, we can simplify the inequality by subtracting 158 from each part:
255 - 158 ≤ 158 + x - 158 ≤ 270 - 158
97 ≤ x ≤ 112
Therefore, the possible values for the 3rd quiz score are between 97 and 112, inclusive.
To solve this problem correctly, you need to know how to calculate an average and manipulate inequalities.