Answer:
The mass of each passenger is 550 kg.
The mass of front decoration is 200 Kg.
Step-by-step explanation:
Given : A roller coaster train with 6 passenger cars and the front decoration has a mass of 3500 kg. when the train has the front decoration and only 4 passenger cars, it has a mass of 2400 kg.
To find : What is the mass of the decoration and of each passenger car?
Solution :
Let the mass of each passenger is x.
Let the mass of front decoration is y.
- When the number of passenger = 6
Mass of 6 passengers and front decoration = 3500 kg.
The equation form is
..........[1]
- When the number of passengers = 4
Mass of 4 passengers and front decoration = 2400 kg.
The equation form is
........[2]
Solving equation [1] and [2]
Subtract equation [2] from [1],
![6x+y-4x-y=3500-2400](https://tex.z-dn.net/?f=6x%2By-4x-y%3D3500-2400)
![2x=1100](https://tex.z-dn.net/?f=2x%3D1100)
![x=550](https://tex.z-dn.net/?f=x%3D550)
Put value in [1],
![6(550)+y=3500](https://tex.z-dn.net/?f=6%28550%29%2By%3D3500)
![3300+y=3500](https://tex.z-dn.net/?f=3300%2By%3D3500)
![y=200](https://tex.z-dn.net/?f=y%3D200)
Therefore, The mass of each passenger is 550 kg.
The mass of front decoration is 200 Kg.