If a patient has a frame costing $200 and an allowance of $100, with a 20% discount on the remaining balance, how much do they pay?

To determine how much the patient pays, we first calculate the amount that is not covered by the allowance. The total cost of the frame is $200, and the allowance is $100.

Subtracting the allowance from the total cost gives us the balance that needs to be covered by the patient:

$200 - $100 = $100

Next, the patient receives a 20% discount on this remaining balance of $100. To find the amount of the discount, we calculate:

20% of $100 = 0.20 × 100 = $20

Now, we subtract the discount from the remaining balance:

$100 - $20 = $80

Therefore, after applying the allowance and the discount, the patient ends up paying $80. This is why the correct answer is $80.