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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 = 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) = = 2464.
Hence, = 2464 + 36 = 2500, and m = = 50.
Then rows = m-6 = 50-6 = 44 and seats = m+6 = 50+6 = 56.
Solved.