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The seats in a theater are arranged in parallel rows that form a rectangular region. The number of seats in each row of the theater is 16 fewer than the number of rows. How many seats are in each row of a theater that has 1,161 seats

Answer :

s - number of seats in a row
r - number of rows

[tex]s+16=r \\sr=1,161 \\ \\s(s+16)=1,161 [/tex]

Since s must be a positive integer, find factors of 1,161.

[tex]1,161:3=387:3=129:3=43[/tex]

[tex]1,161=3^3\times 43=27\times 43[/tex]
[tex]43-27=16[/tex]

Therefore, s = 27.

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