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.

It is stated that the total bill the patient would only pay would be the $25 plus 20% of the original bill. Therefore this would mean that:

25 + 0.2 * X = 200 - - - > 1

25 + 0.2 * X = 800 - - - > 2

Where X represents the original bill.

Calculating for X in equation 1:

25 + 0.2 * X = 200

0.2 * X = 175

X = 875

Calculating for X in equation 2:

25 + 0.2 * X = 800

0.2 * X = 775

X = 3875

Therefore the original bill ranges from $875 to $3875. The equality equation would be:

$875 ≥ X ≥ $3875