Question

A medical 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.

Answer 1

Let the original bill be $x$, then the final bill after the charges been added are $1.2x+25$, where $1.2$ is the increase in the bill by 0.2 (100%+20% = 120% = 1.2)

The range of the original bill is 
200 < $1.2x+25$ < 800, subtract each term by 25
175 < $1.2x$ < 775, divide each term by $1.2$
145.83 < $x$ < 645.83

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