SOLUTION: Solve an Equation: I am having alot of trouble setting up this equation to solve. The owners of a theater plan to reconfigure the seating. Adding 4 rows, they can reduce the numb

Question 434075: Solve an Equation: I am having alot of trouble setting up this equation to solve.
The owners of a theater plan to reconfigure the seating. Adding 4 rows, they can reduce the number of seats per row by 2 without changing capacity. If, instead, they add 5 seats per row, they can reduce the number of rows by 7, thus decreasing capacity by 1 seat. What is the theater's current capacity? (Assume that each row has the same number of seats.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The seating capacity can be expressed as
(number of rows)*(seats/row)
Let = number of rows
Let = number of seats per row
given:
(1)
(2)
--------------------------
(1)
(1)
and
(2)
(2)
------------------
Multiply both sides of (1) by and
multiply both sides of (2) by
Then add the equations
(1)
(2)

and, since
(1)
(1)

Current capacity =
check:
(2)
(2)

OK

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