An auditorium contains 315 occupied seats and was 7/9 filled. How many empty seats were there?
you need to set up a proportion
you say 7 = x
. == ===
9 315
and solve by cross multiplying
(7)x(315)=(9)x(x)
solve for x
by dividing both sides by 9
so
x= (7/9)x 315
use calcualtor
The ratio of occupied seats to. vacants seats in auditorium is 5 to 2 . If there are 120 vacant seats, What is the seating capacity of the auditorium.
An auditorium containing 646 seats was filled 17/19. How many occupied seats were there?
An auditorium containing 646 seats was 17/19 filled. How many occupied seats were there?
Well, if the auditorium was 7/9 filled, it means that 2/9 of the seats were empty. So, to find the number of empty seats, we multiply 2/9 by the total number of seats.
Now, we know there were 315 occupied seats, so let's find the total number of seats. To do this, we can think of the 7/9 filled auditorium as representing 315 seats. We can set up an equation like this:
(7/9) of total seats = 315
To solve for the total number of seats, we can multiply both sides of the equation by the reciprocal of 7/9, which is 9/7.
So, (7/9) of total seats * (9/7) = 315 * (9/7)
Simplifying this, we get:
(63/63) of total seats = 405
Since (63/63) is equal to 1, we can conclude that the total number of seats is 405.
Now, let's find the number of empty seats. We know that 2/9 of the seats were empty, so we can calculate that as follows:
(2/9) of 405 seats = (2/9) * 405
Doing the math, we get:
(2/9) * 405 = 90
Therefore, there were 90 empty seats in the auditorium.
To find the number of empty seats in the auditorium, we first need to determine its total capacity.
Since the auditorium was 7/9 filled, we can assume that 7/9 of the total seats were occupied. Therefore, we can represent the number of occupied seats as 7/9 of the total capacity.
Let's denote the total capacity of the auditorium as "x".
Accordingly, the equation can be set up as follows:
(7/9) * x = 315
To solve for x, we can multiply both sides of the equation by 9/7 to isolate x:
x = (315 * 9) / 7
Evaluating this expression:
x = 405
Therefore, the total capacity of the auditorium is 405 seats.
To find the number of empty seats, we subtract the occupied seats (315) from the total capacity (405):
405 - 315 = 90
Hence, there were 90 empty seats in the auditorium.
(7/9) total = 315
so total = 315 (9/5) = 63*9 = 567
so
empty = 567 - 315 = 252