Answer:
Explanation:
a. To find the scores Shureka must make on the final exam to pass the course with an average of 74 or higher, given that the final exam counts as two tests, you can use the following inequality:
(64 + 71 + 78 + 75 + 2x) / 6 ≥ 74
Here, x represents the score Shureka must achieve on the final exam, and the equation is set up so that the average (total score divided by the number of tests) must be greater than or equal to 74.
Now, let's solve for x:
(64 + 71 + 78 + 75 + 2x) / 6 ≥ 74
(288 + 2x) / 6 ≥ 74
Multiply both sides of the inequality by 6 to eliminate the denominator:
288 + 2x ≥ 444
Subtract 288 from both sides:
2x ≥ 444 - 288
2x ≥ 156
Now, divide by 2:
x ≥ 156 / 2
x ≥ 78
So, Shureka must score 78 or higher on her final exam to pass the course with an average of 74 or higher.
b. The answer to part (a) means that in order to achieve an average score of 74 or higher for the course, Shureka needs to score at least 78 on her final exam. If she scores below 78 on the final exam, her average will fall below 74, and she may not pass the course. In essence, this answer tells Shureka the minimum performance required on the final exam to meet her desired course average.