¾ of the seats in a concert hall were occupied. The ratio of adults to children was 7 : 3. If 90 more adults attended the concert, the number of adults would be 3 times the number of children. How many seats were in the concert hall?
in each 10, there are 7 adults, and three children
(A+90)=3C
but A/C=7/3 or A=7C/3
7C/3 + 90=3C
2/3 C=90
C=135
A=7/3 135=7(45)= you do it.
Finally, number of concert seats.
3/4 Seats= A+C solve for Seats
84
To find the number of seats in the concert hall, we need to analyze the information given step by step.
Let's assume there are a total of x seats in the concert hall.
We are told that ¾ of the seats were occupied. This means that (3/4)x seats were occupied.
The ratio of adults to children was given as 7:3. This means that for every 7 adults, there were 3 children.
Let's assume there were 7a adults and 3c children in the concert hall. So the total number of occupied seats becomes 7a + 3c.
We also know that if 90 more adults attended the concert, the number of adults would be 3 times the number of children. So we have the equation:
7a + 90 = 3c
Now, let's combine the information we have:
7a + 3c = (3/4)x ----(1) (from the given occupancy rate)
7a + 90 = 3c ----(2) (from the information about additional adults)
To solve these two equations, we can use the method of substitution.
From equation (2), we can rearrange it as:
7a - 3c = -90
Now, we can multiply it by 3:
21a - 9c = -270 ----(3)
We can rewrite equation (1) as:
28a + 12c = 3x ----(4)
Now, we can multiply equation (2) by 4:
28a + 12c = 360 ----(5)
Now, we can subtract equation (5) from equation (4):
(28a + 12c) - (28a + 12c) = 3x - 360
0 = 3x - 360
3x = 360
x = 360/3
x = 120
Therefore, there were 120 seats in the concert hall.