100-point tests, Erica has scored 76,84 , and 78

Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Erica has scored 76, 84, and 78 on the first three. What range of scores on the fourth test will give Erica 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

To find MINIMUM test grade, we need to use the MINIMUM value of the C average (70)

76 + 84 + 78 + x

---------------------- = 70

4

76 + 84 + 78 + x = 280

238 + x = 280

x = 42, the lowest grade she can get on her fourth test to maintain a C average.

To find MAXIMUM test grade, we need to use the MAXIMUM value of the C average (79)

76 + 84 + 78 + x

---------------------- = 79

4

76 + 84 + 78 + x = 316

238 + x = 316

x = 78, the highest test grade she can get on her fourth test to maintain a C average.

42 </ x </ 78