**Question:**

To receive grade A in a course one must obtain an average of 90 marks or more in five papers, each of 100 marks. If Tanvy scored 89, 93, 95 and 91 marks in first four papers, find the minimum marks that she must score in the last paper to get grade A in the course.

**Solution:**

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.