Andy C. answered • 09/08/17

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r is the number of rows

c is the number of seats in each row (or COLUMNS)

r x c = 252 ---> r = 252/c

(r-2) x (c + 3) = 252

(252/c - 2) x (c + 3) = 252

(252 - 2c)(c+3) = 252c <--- multiplies everything by c to clear the fractions

252c - 2c^2 + 756 - 6c = 252c

-2c^2 + 756 - 6c = 0 <--- subtracts 252c from both sides

2c^2 + 6c - 756 = 0 <--- multiplies both sides by -1 to change the signs so that the leading coefficient is positive

c^2 + 3c - 378 = 0

( c -18 )( c +21 ) = 0

c-18 = 0 --> c = 18

c+21 = 0 ---> c=-21 <--- rejected; negative # of seats not allowed

**There were 18 seats in each row, so 252/18 = 14 rows**

If there are 21 seats in each row, then 252/21 = 12 rows.