Question

The Loft Theater has a center seating section with 3c + 8 rows and 4c-1 seats in each row. Write an expression for the total number of seats in the center section.

Answer 1

If there are n rows

And if each row has m seats.

Then the total number of seats shall be n × m.

Here

Number of rows = (c+8)

And number of seats in each row = (4c-1)

Using the concept

Total number of seats

= (c+8)(4c-1)

FOILing or Distributing we get

= c(4c) + c (-1) + 8(4c) +8 (-1)

= 4c² - c + 32 c -8

Combining like terms

=4c² +31c - 8

The expression for total number of seats = 4c² + 31c -8