Answer:
44 seats in each row
Problem:
A rectangular auditorium seats 1144 people. The number of seats in each row exceeds the number of rows by 18. Find the number of seats in each row.
Explanation:
Let n be the number of rows.
If the number of seats exceed the number of rows by 18, then the number ot seats can be represented by n+18.
So we have a n by n+18 rectangle whose number of seats in all is 1144.
So we need to solve n(n+18)=1144
Distribute: n^2+18n=1144
Subtract 1144 on both sides" n^2+18n-1144=0
What two numbers multiply to be -1144 but also add to be 18?
Hmmm.. let's break -1144 down a little into smaller factors.
-1144=2(-572)=4(-286)=8(-143)=-8(13)(11)=-26(44)
We found a pair of factors that will work? -26 and 44.
So the factorization of our quadratic equation is (n-26)(n+44)=0.
This implies either n-26=0 or n+44=0 .
n=26 by adding 26 on both sides for first equation.
n=-44 by subtracting 44 on both sides for second equation.
n=26 is the only one that works.
This means there are 26 rows and 26+18 seats in each row.
26 rows
44 seats in each row
That product does equal 1144 seats in all.