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 [tex]6x+y=3500[/tex] ..........[1]
- When the number of passengers = 4
Mass of 4 passengers and front decoration = 2400 kg.
The equation form is [tex]4x+y=2400[/tex] ........[2]
Solving equation [1] and [2]
Subtract equation [2] from [1],
[tex]6x+y-4x-y=3500-2400[/tex]
[tex]2x=1100[/tex]
[tex]x=550[/tex]
Put value in [1],
[tex]6(550)+y=3500[/tex]
[tex]3300+y=3500[/tex]
[tex]y=200[/tex]
Therefore, The mass of each passenger is 550 kg.
The mass of front decoration is 200 Kg.
