A train broke down and the passengers had to leave the train and take buses to continue their journey. When the first bus came, ¼ of the passengers tried to board, but 4 of them were not able to get on. When the second bus came, ½ of the remaining passengers tried to board, but 6 of them were not able to get on. When the third bus came, ¾ of the remaining passengers boarded. There were still 8 passengers left stranded. How many passengers were on the train?

There were 64 passengers on the trainStep-by-step explanation:A train broke down and the passengers had to leave the train and take buses to continue their journeyWhen the first bus came, ¼ of the passengers tried to board, but 4 of them were not able to get onWhen the second bus came, ½ of the remaining passengers tried to board, but 6 of them were not able to get onWhen the third bus came, ¾ of the remaining passengers boardedThere were still 8 passengers left strandedWe need to know how many passengers were on the trainAssume 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 = 64There were 64 passengers on the trainLearn more:You can learn more about fractions in brainly.com/question/8520610#LearnwithBrainly