# Thread: Find the number of rows of seats

1. ## Find the number of rows of seats

A multimedia library as 108 seats, which are all arranged in rows. The number of seats in each row is 3 less than the number of rows. How many rows of seats are in the library?

The answer appears to be 12 but I can't figure out how to set up an equation with variables and solve for this.

2. ## Re: Find the number of rows of seats

Originally Posted by dannyc
A multimedia library as 108 seats, which are all arranged in rows. The number of seats in each row is 3 less than the number of rows. How many rows of seats are in the library?

The answer appears to be 12 but I can't figure out how to set up an equation with variables and solve for this.
let there be y rows. then there are y-3 seats in each row. hence (y-3)y=108.

3. ## Re: Find the number of rows of seats

Originally Posted by dannyc
A multimedia library as 108 seats, which are all arranged in rows. The number of seats in each row is 3 less than the number of rows. How many rows of seats are in the library?
Try $n(n-3)=108.$

4. ## Re: Find the number of rows of seats

Ah yes, that certainly works! Thanks abhishekkgp and Plato! But why do we multiply?

5. ## Re: Find the number of rows of seats

Originally Posted by dannyc
Ah yes, that certainly works! Thanks abhishekkgp and Plato! But why do we multiply?
Count the number of dots below:

.....
.....
.....

Counting one by one you get 15. But a smarter way would be to observe that there are 5 dots in each row and there are a total of 3 rows. hence 5x3=15. Now do u get it?

6. ## Re: Find the number of rows of seats

Oh yes of course, I can't believe I didn't realize that! Thank you again!