Amedical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. if the average bill for a patient is between $200 and $800, find the range of the original bill.

Let the original bill be , then the final bill after the charges been added are , where  is the increase in the bill by 0.2 (100%+20% = 120% = 1.2)

The range of the original bill is 
200 <  < 800, subtract each term by 25
175 <  < 775, divide each term by 
145.83 <  < 645.83

Hence, the range of the original bill is between $145.83 and $645.83