Question:
To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita’s marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade ‘A’ in the course.
Solution:
Let x be the marks obtained by Sunita in the fifth examination.
In order to receive grade ‘A’ in the course, she must obtain an average of 90 marks or more in five examinations.
Therefore,
$\frac{87+92+94+95+x}{5} \geq 90$
$\Rightarrow \frac{368+x}{5} \geq 90$
$\Rightarrow 368+x \geq 450$
$\Rightarrow x \geq 450-368$
$\Rightarrow x \geq 82$
Thus, Sunita must obtain greater than or equal to 82 marks in the fifth examination.