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 Sunitas marks in first four examinations are $87,92,94$ and $95$, find minimum marks that Sunita must obtain in the fifth examination to get grade $A$ in the course.

Answer 1

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,
$\frac{87+92+94+95+x}{5}\ge 90$
$\Rightarrow \frac{368+x}{5}\ge 90$
$\Rightarrow 368+x\ge 450$
$\Rightarrow x\ge 450-368$
$\Rightarrow x\ge 82$
Thus sunita must obtain greater than or equal to $82$ marks in the fifth examination.