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

Answer: The mass of each passenger is 550 kg.

The mass of front decoration = 200 Kg.

Step-by-step explanation:

Let the mass of each passenger be 'x'.

Let the mass of front decoration be 'y'.

So, Number of passenger = 6

Mass of 6 passengers and front decoration = 3500 kg.

Number of passengers = 4

Mass of 4 passengers and front decoration = 2400 kg.

According to question, it becomes,

$6x+y=3500\\\\\implies y=3500-6x----------------(1)\\\\4x+y=2400\\\\\implies y=2400-4x---------------(2)$

so, From Eq(1) and Eq(2), we have,

$3500-6x=y=2400-4x\\\\3500-6x=2400-4x\\\\3500-2400=-4x+6x\\\\1100=2x\\\\x=\frac{1100}{2}=550$

Hence, the mass of each passenger is 550 kg.

The mass of front decoration = 3500-550(6)=200 Kg.