Question 1040539
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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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<pre>
It is boring to solve a quadratic equation for this case.

I'd better calculate {{{sqrt(2464)}}} = 49.6.

So, I think the answer is 56 and 44.

56*44 = 2464 !!!   Correct !!!
</pre>

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.


<pre>
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^2 - 36}}} = 2464.

Hence, {{{m^2}}} = 2464 + 36 = 2500,  and  m = {{{sqrt(2500)}}} = 50.

Then rows = m-6 = 50-6 = 44  and seats = m+6 = 50+6 = 56.
</pre>

Solved.