SOLUTION: A rectangular auditorium seats 2464 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row.

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Question 1040539: A rectangular auditorium seats 2464 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row.
Answer by ikleyn(52781) About Me  (Show Source):
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A rectangular auditorium seats 2464 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row.
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It is boring to solve a quadratic equation for this case.

I'd better calculate sqrt%282464%29 = 49.6.

So, I think the answer is 56 and 44.

56*44 = 2464 !!!   Correct !!!

By the way, the quadratic equation is n*(n+12) = 2464,

and you can solve it on your own to find "n", the number of rows.

Hope you will get the answer n = 44. 

There is one more way to solve the problem and to avoid boring calculations.

Let "m" be an unknown number which is 6 more than the number of rows: rows = m -6.

Then "m" is 6 less then the number of seats in a row: seats = m+6.

The product seats*rows = (m+6)*(m-6) = m%5E2+-+36 = 2464.

Hence, m%5E2 = 2464 + 36 = 2500,  and  m = sqrt%282500%29 = 50.

Then rows = m-6 = 50-6 = 44  and seats = m+6 = 50+6 = 56.

Solved.