word problem algebra

12dlsam

A cinema contains 315 seats. It has x numbers of rows with an equal number of seats in each row. Six rows of seats are removed to create a fire escape. To ensure the same capacity, the number of seats per row must be increased by six.
How many rows of seats did the cinema originally have??

Can anyone please help with the above question, thanks in advance

Yakuza

Assume there are y seats per row.
In the original configuration, the total number of seats is x * y = 315
Under the new configuration, the total number of seats is (x-6) * (y+6).

Set these equal and solve (you will end up with a quadratic).

12dlsam

so do you mean x*y = (x-6)*(y+6)?? Im not getting a quadratic from this??

Yakuza

You're on the right track.
x*y = (x-6)*(y+6)
x*y = x*y +6x -6y - 36.
Remove x*y from both sides, you're left with:
0 = +6x -6y -36.
Re-arrange:
6y+36 = 6x.
Simplify:
y+6 = x.

Now, remember we had x*y = 315?
Plug in x = y+6. into this, you get
(y+6) * y = 315.
Multiply out and re-arrange:
y² + 6y - 315 = 0.
There's your quadratic