Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Gloria has scored 90, 80, and 84 on the first three. What range of scores on the fourth test will give Gloria a C for the semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value. Express your answer in interval notation.

a) [65, 75]
b) [60, 70]
c) [68, 78]
d) [72, 82]

Answer 1

To achieve a C for the semester, Gloria's score on the fourth test should be between 65 and 75.

Step-by-step explanation:

The final course grade depends entirely on the average of four equally weighted 100-point tests. In order for Gloria to achieve a C for the semester (an average between 70 and 79, inclusive), we need to find the range of scores she can get on the fourth test.

To calculate the range, we need to find the lowest possible score on the fourth test that would give Gloria an average score of 70 for all four tests, as well as the highest possible score on the fourth test that would give her an average score of 79.

Since the fourth test is equally weighted as the other three, we can calculate the average score of the first three tests by summing them and dividing by 3. From this, we can determine the range of scores on the fourth test that would give Gloria a C for the semester to be between 65 and 75. Therefore, the answer is option a) [65, 75].