Assume that all test scores have a non-negative value. Express your answer in interval notation.

Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Sarah has scored 89, 92, and 82 on the first three. What range of scores on the fourth test will give Sarah a B for the semester (an average between 80 and 89, inclusive)? Assume that all test scores have a non-negative value.

Express your answer in interval notation.

Answer 1

let x be the test score for the fourth test

then (89 + 92 + 82 + x)/4 is her average test score

so, we need 80 ≤ (89 + 92 + 82 + x)/4 ≤ 89

solve the inequality for x

80 ≤ (89 + 92 + 82 + x)/4 ≤ 89

320 ≤ 263 + x ≤ 356

57 ≤ x ≤ 93

then the range of scores in interval notation is [57,93]