To receive grade A in a course one must obtain an average of 90 marks

Let x marks be scored by Tanvy in her last paper.

It is given that Tanvy scored 89, 93, 95 and 91 marks in first 4 papers.

To receive grade A, she must obtain an average of 90 marks or more.

Therefore,

$\frac{89+93+95+91+x}{5} \geq 90$

Multiplying both the sides by 5 in the above equation

$\left(\frac{89+93+95+91+x}{5}\right)(5) \geq 90(5)$

368 + x ≥ 450

Subtracting 368 from both the sides in the above equation

$368+x-368 \geq 450-368$

$x \geq 82$

Therefore, Tanvy should score minimum of 82 marks in her last paper to get grade A in the course.