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 f
inal grade of b. devon's grades on the first four tests were 92%, 82%, 88%, and 92%. what range of grades on the fifth test would give him a b in the course?
<span>46 <= grade < 96
First, let's write the equation for the lower limit that the student must get for a B.
(x + 92 + 82 + 88 + 92)/5 = 80
Multiply both sides by 5 giving
x + 92 + 82 + 88 + 92 = 400
Subtract 92, 82, 88, 92 from both sides
x = 400 - 92 - 82 - 88 - 92 = 46
So the student has to get 46 or higher on the test to make a B.
Now let's compute the upper limit
(x + 92 + 82 + 88 + 92)/5 < 90
Multiply both sides by 5
(x + 92 + 82 + 88 + 92) < 450
Subtract 92, 82, 88, 92 from both sides
x < 450 - 92 - 82 - 88 - 92 ) = 96
So the student has to get a grade of less than 96 to get a B.</span>
