100-point tests, Erica has scored 94, 82, and 91 on the first three.

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 94, 82, and 91 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

94, 82, 91 have an average of (94+82+91)/3= 267/3 = 89

to get a C, 70 to 79 average requires (94+82+91+x)/4 >70

267+x>280

x > 13

and

(94+82+91+x)/4<79

267+ x< 316

x < 49

to get a C you need a 4th test grade between 13 and 49

13 < x < 49

or

x is in the interval [13, 49]

brackets mean the interval includes the endpoints