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 75, 80, and 91 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.

Answer 1

Scores between 34 and 70 on the fourth test will give Paul a C for the semester.

Explanation:

The average is given by the sum of all scores divided by the number of scores.

In this question:

Sum of all scores: 75 + 80 + 91 + x = 246 + x

Number of tests : 4

Grade of 70:

`(246 + x)/(4) = 70`

`246 + x = 280`

`x = 280 - 246`

`x = 34`

Grade of 79:

`(246 + x)/(4) = 79`

`246 + x = 316`

`x = 316 - 246`

`x = 70`

Scores between 34 and 70 on the fourth test will give Paul a C for the semester.