Range of inequalities

Question

Karl’s grades on his first five exams are 71, 65, 72, 80, and 77. What range of scores can Karl earn on his sixth exam so that his final grade is a C? All of the exams have a maximum score of 100. A final grade of C is given when the test average is greater than or equal to 70 and less than 80.

Answer 1

To answer this question you need to use two equations, one for the higher limit and one for the lower limit. If you take the scores he has right now his final grade would be a 73. I got this by finding the average of all the tests. Since you want to add one more test you change the format to add the sixth exam (x) as a variable.

Therefore to help find the lower limit: (x + 71 + 65 + 72 + 80 + 77)/6  = 70

From there you solve for x, and do something similar to reach the upper limit.