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Q.
Ravi obtained $70$ and $75$ marks in first two unit tests. Then, the minimum marks he should get in the third test to have an average of atleast $60$ marks, are
Linear Inequalities
Solution:
Let Ravi got $x$ marks in third unit test.
$\therefore$ Average marks obtained by Ravi
$=\frac{\text { Sum of marks in all tests }}{\text { Number of tests }} $
$ =\frac{70+75+x}{3}=\frac{145+x}{3}$
Now, it is given that he wants to obtain an average of atleast 60 marks.
Atleast 60 marks means that the marks should be greater than or equal to 60 .
$\text { i.e., } \frac{145+x}{3} \geq 60 $
$\Rightarrow 145+x \geq 60 \times 3$
$\Rightarrow 145+x \geq 180$
Now, transferring the term 145 to $RHS$,
$x \geq 180-145 $
$\Rightarrow x \geq 35$
i.e., Ravi should get greater than or equal to 35 marks in third unit test to get an average of atleast 60 marks.
$\therefore$ Minimum marks Ravi should get $=35$