Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests,

Paul has scored 91, 88, and 93 on the first three. What range of scores on the fourth test will give Paul 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.

Answer 1

[8, 44]

Explanation:

The average of equally-weighted values is their sum divided by their number.

Setup

For some fourth test score x, Paul wants an average between 70 and 79. This gives rise to the inequality ...

70 ≤ (91 +88 +93 +x)/4 ≤ 79

Solution

Multiplying by 4, we have ...

280 ≤ 272 +x ≤ 316

8 ≤ x ≤ 44 . . . . . . . . . . subtract 272

Paul will get a C if his fourth test score is in the interval [8, 44].