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in Algebra by (47.4k points)
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The number of seats in a row is equal to the total number of rows in a hall. The total number of seats in the hall will increase by 375 if the number of rows is doubled and the number of seats in each row is reduced by 5. Find the number of rows in the hall at the beginning.

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Best answer

Let the no of seats in each row be x

⇒ 2x2 – 10x = x2 + 375

⇒ x2 – 10x – 375 = 0

⇒ x2 – 25x + 15x – 375 = 0

⇒ x (x – 25) + 15 (x – 25) = 0

⇒ (x – 25) (x + 15) = 0

⇒ x = 25, x = -15, x > 0

∴ 25 rows are in the hall

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