Let x be the grade of the last exam, then the average is:
[tex]\frac{71+76+88+92+x}{5}=\frac{x+327}{5}[/tex]
now, to get a B we need this to be greater or equal than 80 and less than 90, that is:
[tex]80\leq\frac{x+327}{5}<90[/tex]
Solving for x we have:
[tex]\begin{gathered} 80\leq\frac{x+327}{5}<90 \\ 5\cdot80\leq x+327<5\cdot90 \\ 400\leq x+327<450 \\ 400-327\leq x<450-327 \\ 73\leq x<123 \end{gathered}[/tex]
Therefore the range of grades on the fifth exam that results in earnings a B is
[tex]73\leq x<123[/tex]
If the highest grade is 100, then
[tex]73\leq x\leq100[/tex]
