Answer
The student must earn at least 92 grades.
Work Step by Step
Consider the value of the grades in the fourth examination to be x.
The grades in the first 3 examinations are 76, 80, and 72. The total of the grades of these 4 examinations is divided by 4 to get an average. Thus,
\[\begin{align}
& \frac{76+80+72+x}{4}\ge 80 \\
& \frac{228+x}{4}\ge 80 \\
& 228+x\ge 320 \\
& x\ge 92
\end{align}\]
The student must score at least 92 grades in the fourth examination so as to have an average of at least 80.
Hence, the student must earn at least 92 grades in the fourth examination so as to have an average of at least 80.
