# To receive Grade $'A'$ in a course, one must obtain an average of $90$ marks or more in fine. examination (each of $100$ marks ) . If sunita's mark in first four examinations are $87,92,94$ and $95$ find the minimum marks that sunita must obtains in the fifth examination to get grade $'A'$ in the corse

$\begin{array}{1 1} (A)\;78 \\(B)\;35 \\(C)\;56 \\(D)\;82 \end{array}$

Toolbox:
• Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
• Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
• If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $'>'$ sign changes to $'<'$ and $'<'$ changes $'>'$ .
Let x be the marks sunita obtained in the fifth examination.
Total marks obtained in all five examination is
$87 +92+94 +95+x$
To get grade A the average must be greater than or equal 90.
Thus $\large\frac{87 +92+94 +95+x}{5} $$\geq 90 => \large\frac{368 +x}{5}$$ \geq 90$
Multiplying both sides by positive number 5.
$=> 368 +x \geq 450$
Subtracting 368 from both sides,
$=> x \leq 450 -368$
$=> x \geq 82$
Step 2:
Sunitha must obtain atleast 82 marks to get grade A.
Hence D is the correct answer.