There were 64 passengers on the train
Step-by-step explanation:
A train broke down and the passengers had to leave the train and take buses to continue their journey
We need to know how many passengers were on the train
Assume that there were x passengers in the train
∵ There were x passengers in the train
∵ [tex]\frac{1}{4}[/tex] of the passengers tried to board on the 1st bus
∴ [tex]\frac{1}{4}[/tex] x tried to board on the 1st bus
∴ The remaining = x - [tex]\frac{1}{4}[/tex] x = [tex]\frac{3}{4}[/tex] x
∵ 4 passengers of ¼ of the passengers tried to board were not
able to get on
∴ The remaining after 1st bus = [tex]\frac{3}{4}[/tex] x + 4
∵ ½ of the remaining passengers after 1st bus tried to board
on the 2nd bus
∴ The remaining after the 2nd bus is ½ of the remaining after the
1st bus ⇒ (1 - ½ = ½)
∴ The remaining after the 2nd bus = [tex]\frac{1}{2}[/tex] ( [tex]\frac{3}{4}[/tex] x + 4 )
∵ 6 passengers of ½ of the remaining passengers tried to board
were not able to get on
∴ The remaining after the 2nd bus = [tex]\frac{1}{2}[/tex] ( [tex]\frac{3}{4}[/tex] x + 4 ) + 6
- Simplify the expression
∴ The remaining after the 2nd bus = ( [tex]\frac{3}{8}[/tex] x + 2 ) + 6
- Add like terms
∴ The remaining after the 2nd bus = [tex]\frac{3}{8}[/tex] x + 8
∵ ¾ of the remaining passengers boarded on the 3rd bus
∴ The remaining after the 3rd bus is ¼ of the remaining after the
2nd bus ⇒ (1 - ¾ = ¼)
∴ The remaining after the 3rd bus = [tex]\frac{1}{4}[/tex] ( [tex]\frac{3}{8}[/tex] x + 8 )
- Simplify the expression
∴ The remaining after the 3rd bus = [tex]\frac{3}{32}[/tex] x + 2
∵ There were still 8 passengers left stranded
- Equate the expression of remaining after the 3rd bus by 8
∴ [tex]\frac{3}{32}[/tex] x + 2 = 8
- Subtract 2 from both sides
∴ [tex]\frac{3}{32}[/tex] x = 6
- Multiply both sides by 32
∴ 3 x = 192
- Divide both sides by 3
∴ x = 64
There were 64 passengers on the train
Learn more:
You can learn more about fractions in brainly.com/question/8520610
#LearnwithBrainly
