Question 1179481
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The standard algebraic solution shown by the other tutor uses x and x+6 for the two numbers whose difference is 6; that leads to a solution in which you need to factor the quadratic equation<br>
{{{x^2+6x-247=0}}}<br>
It will be difficult for most people to find that the correct factorization is<br>
{{{(x+19)(x-13)=0}}}<br>
leading to an answer of 13 rows of 19 seats each.<br>
Here is a technique that can be used to make an algebraic solution easier in this and many similar problems.<br>
Let the number of rows be x-3 and the number of seats in each row be x+3.<br>
Note the difference of 6 between the two numbers was implemented by letting x be halfway between the two numbers.<br>
Now the equation is solved much more easily:<br>
{{{(x-3)(x+3)=247}}}
{{{x^2-9=247}}}
{{{x^2=256}}}
{{{x=16}}}<br>
ANSWER: The number of rows is x-3=13<br>