SOLUTION: A theater can seat 247 people. The number of rows is 6 less than the number of seats in each row. How many rows of seats are there?

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Question 1179481: A theater can seat 247 people. The number of rows is 6 less than the number of seats in each row. How many rows of seats are there?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Write an equation as you read the problem

    r*(r+6) = 247


Now solve it, simplifying step by step

    r^2 + 6r - 247 = 0

    (r+19)*(r-13) = 0   (after factoring)



The roots are -19 and 13, and from these two roots we choose the positive value 13 as the only one solution, which makes sense.



ANSWER.  13 rows.


Solved, answered, explained and completed.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


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



It will be difficult for most people to find that the correct factorization is



leading to an answer of 13 rows of 19 seats each.

Here is a technique that can be used to make an algebraic solution easier in this and many similar problems.

Let the number of rows be x-3 and the number of seats in each row be x+3.

Note the difference of 6 between the two numbers was implemented by letting x be halfway between the two numbers.

Now the equation is solved much more easily:






ANSWER: The number of rows is x-3=13
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