Answer:
Number of box seats = 1000
Number of lower deck seats = 5000
Number of upper deck seats = 4000
Step-by-step explanation:
Let number of box seats = ![x](https://tex.z-dn.net/?f=x)
Let number of lower deck seats = ![y](https://tex.z-dn.net/?f=y)
Let number of upper deck seats = ![z](https://tex.z-dn.net/?f=z)
As per question statement:
...... (1)
Cost for box seat = $10
Cost for
box seats = 10![x](https://tex.z-dn.net/?f=x)
Cost for lower deck seat = $8
Cost for
lower deck seats = 8![y](https://tex.z-dn.net/?f=y)
Cost for lower deck seat = $5
Cost for
lower deck seats = 5![z](https://tex.z-dn.net/?f=z)
As per question statement:
..... (2)
..... (3)
Putting value of
in (1) and (2):
....... (4)
![10x+8 y+5\times 4x=70000\\\Rightarrow 30x+8y=70000 ..... (5)](https://tex.z-dn.net/?f=10x%2B8%20y%2B5%5Ctimes%204x%3D70000%5C%5C%5CRightarrow%2030x%2B8y%3D70000%20.....%20%285%29)
8
(4) - (5):
10000
![\Rightarrow x = 1000](https://tex.z-dn.net/?f=%5CRightarrow%20x%20%3D%201000)
By (3):
![z = 4000](https://tex.z-dn.net/?f=z%20%3D%204000)
Now, by equation (1):
= 5000
Number of box seats = 1000
Number of lower deck seats = 5000
Number of upper deck seats = 4000