Madoka has scores 84, 89, and 91, each out of 100 points, on her algebra tests. Use an inequality to find the score she must make on the final exam to pass the course with an average of 90 percent or higher, given that the final is worth 150 points.
To find the score Madoka must make on the final exam to pass the course with an average of 90 percent or higher, we can set up an inequality.
First, let's calculate Madoka's current average score.
The first test score is 84 out of 100, the second test score is 89 out of 100, and the third test score is 91 out of 100.
To find the average, we add all three scores and divide by the total number of scores:
(84 + 89 + 91) / 3 = 88
Madoka's current average score is 88.
Now, we can set up the inequality. Let x be the score Madoka gets on the final exam (out of 150 points).
To find her average score, we need to calculate the total points Madoka will have after the final exam:
Total points = current average score x number of tests + score on final exam
Total points = 88 * 3 + x
To pass the course with an average of 90 percent or higher, the average score must be equal to or greater than 90. So we have:
(88 * 3 + x) / 4 ≥ 90
Now, we can solve this inequality for x:
(88 * 3 + x) / 4 ≥ 90
262 + x ≥ 360 (multiply both sides of the inequality by 4)
x ≥ 360 - 262
x ≥ 98
To pass the course with an average of 90 percent or higher, Madoka must score 98 or higher on the final exam.