Let the original bill be [tex]x[/tex], then the final bill after the charges been added are [tex]1.2x+25[/tex], where [tex]1.2[/tex] is the increase in the bill by 0.2 (100%+20% = 120% = 1.2)
The range of the original bill is
200 < [tex]1.2x+25[/tex] < 800, subtract each term by 25
175 < [tex]1.2x[/tex] < 775, divide each term by [tex]1.2[/tex]
145.83 < [tex]x[/tex] < 645.83
Hence, the range of the original bill is between $145.83 and $645.83