In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Sarah has scored 90 , 91 , and 85 on the first three. What range of scores on the fourth test will give Sarah 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.

To find the range of scores on the fourth test that will give Sarah a C for the semester, we need to calculate the minimum and maximum average scores she can achieve. The minimum average score for Sarah to get a C is when she scores the lowest possible score on the fourth test. In this case, her average score would be (90 + 91 + 85 + x) / 4, where x is the score on the fourth test. Setting this expression equal to 70 and solving for x, we get: (90 + 91 + 85 + x) / 4 = 70 266 + x = 280 x = 14 So, the minimum score Sarah can get on the fourth test to achieve a C is 14. The maximum average score for Sarah to get a C is when she scores the highest possible score on the fourth test. In this case, her average score would be (90 + 91 + 85 + x) / 4, where x is the score on the fourth test. Setting this expression equal to 79 and solving for x, we get: (90 + 91 + 85 + x) / 4 = 79 266 + x = 316 x = 50 So, the maximum score Sarah can get on the fourth test to achieve a C is 50. Therefore, the range of scores on the fourth test that will give Sarah a C for the semester is [14, 50].