On solving the equation for the given situation, there are [tex]140[/tex] cars in the train.
Let the total number of cars in the train be [tex]x[/tex].
Half of the cars on a train are flat cars.
So, number of flat cars [tex]= \frac{x}{2}[/tex].
The train has half as many coal cars as flat cars.
So, number of coal cars [tex]= \frac{x}{4}[/tex].
The train has one-fifth as many passenger cars as coal cars.
So, number of passenger cars [tex]= \frac{x}{4}\times \frac{1}{5}=\frac{x}{20}[/tex].
Other cars [tex]= 28[/tex].
Now, according to question,
[tex]x=\frac{x}{2}+\frac{x}{4}+\frac{x}{20}+28[/tex]
[tex]x=\frac{10x+5x+x}{20}+28[/tex]
[tex]x=\frac{16x}{20}+28[/tex]
[tex]x-\frac{16x}{20}=28[/tex]
[tex]\frac{20x-16x}{20}=28[/tex]
[tex]\frac{4x}{20}=28[/tex]
[tex]\frac{x}{5}=28[/tex]
[tex]x=28\times 5[/tex]
[tex]x=140[/tex]
So, there are [tex]140[/tex] cars in the train.
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