Question

A theatre having 1200 seats all of wich are either balcony or ochrestra seat has 250 fewer balcony seats than orchestra seats how many balcony seats are there?

Answer 1

Answer: There are 475 balcony seats.

Explanation:

Let be "b" the number of balcony seats in the theater and "o" the number of ochrestra seats in the theater.

Set up a system of equations:

`\left \{ {{b+o=1200} \atop {b=o-250}} \right.`

Applying the Subsitution method, you can solve for "o" from the first equation:

`o=1200-b`

Now substitute this into the second one and solve for "b", in order to find its value:

`b=(1200-b)-250\\\\2b=950\\\\b=(950)/(2)\\\\b=475`