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The number of rows in a lecture hall equals the number of seats in a row. If the number of rows is doubled and the
number of seats in every row is reduced by 10 , the number ofseats is increased by 300 . If $x$ denotes the number of rows in the lecture hall, then what is the value of $x$ ?
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number of seats in every row is reduced by 10 , the number ofseats is increased by 300 . If $x$ denotes the number of rows in the lecture hall, then what is the value of $x$ ?
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Verified Answer
The correct answer is:
30
As given $\Rightarrow$ Number of seats in each row $=x$ Total number of seats in the hall $=x$ Revised number of rows $=2 x$ Revised number in each row $=x-10$ Thus Revised number of seats $=2 x(x-10)=2 x^{2}-20 x$ According to question,
$\Rightarrow x^{2}-20 x-300=0$
$\Rightarrow x^{2}-30 x+10 x-300=0$
$(x-30)(x+10)=0$
$\Rightarrow x=30$
$(\because \quad x \neq-10)$
$\Rightarrow x^{2}-20 x-300=0$
$\Rightarrow x^{2}-30 x+10 x-300=0$
$(x-30)(x+10)=0$
$\Rightarrow x=30$
$(\because \quad x \neq-10)$
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