Question

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. what is the mass of the decoration and of each passenger car?

Answer 1

The mass of each passenger is 550 kg.

The mass of front decoration is 200 Kg.

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
`6x+y=3500` ..........[1]

• When the number of passengers = 4

Mass of 4 passengers and front decoration = 2400 kg.

The equation form is
`4x+y=2400` ........[2]

Solving equation [1] and [2]

Subtract equation [2] from [1],

`6x+y-4x-y=3500-2400`

`2x=1100`

`x=550`

Put value in [1],

`6(550)+y=3500`

`3300+y=3500`

`y=200`

Therefore, The mass of each passenger is 550 kg.

The mass of front decoration is 200 Kg.