Chapter 6.5, Problem 57E

A Grade of B In Example 9 on page 320, what range of grades on the fifth test would result in Devon receiving a grade of B if his grades on the first four tests were 78%, 64%, 88%, and 76%?

Example 9 Average Grade

1. A.    student must have an average (the mean) on five tests that is greater than or equal to 80% but less than 90% to receive a final grade of
2. B.     Devon s grades on the first four tests were 98%, 76%, 86% and 92%. What range of grades on the fifth test would give him a B in the course.

Solution

The unknown quantity is the range of grades on the fifth test First construct an inequality that can be used to find the range of grades on the fifth test. The average (mean) is found by adding the grades and dividing the sum by the number of tests.

Let x = the filth grade, Then

$Average=\frac{98+76+86+92+x}{5}$

For Devon to obtain a B in this course, his average must be greater than or equal to 80 but less than 90.

Thus, a grade greater than or equal to 48% and less than 98% on the fifth test will result in Devon getting a grade of B in this course.