Answer:
a). At least 99 marks should be scored by the student to get an A.
b). Student has to score at least 59 and less than 99 grades in the 4th exam to get a B.
Step-by-step explanation:
Student's grades on the first three exams are 85, 87, and 89.
Since student's course grade is to be determined by averaging 4 exams.
So average of 4 exams = [tex]\frac{85+87+89+x}{4}[/tex]
Here x is the grade obtained by the student in 4th exam.
If the average of 4 exams to get an A is at least 90 so the expression will be
[tex]\frac{85+87+89+x}{4}\geq 90[/tex]
[tex]\frac{261+x}{4}\geq 90[/tex]
261 + x ≥ 360
x ≥ 360 - 261
x ≥ 99
At least 99 marks should be scored by the student to get an A.
To get a B (Average of at least 80) the expression will be
[tex]80\leq \frac{85+87+89+x}{4}< 90[/tex]
[tex]320\leq(261+x)< 360[/tex]
320-261 ≤ x < 360-261
59 ≤ x < 99
Therefore, student has to score at least 59 and less than 99 grades in the 4th exam to get a B.
