Let's break down the information provided and fill in the blanks to write the equation.
We know that Stan tipped the waiter 20% on the reduced bill, which was a $15 tip. This means that the $15 tip is equal to 20% of the reduced bill.
We need to find the reduced bill first. We are told that the friend told the waiter to remove the $12 dessert from Stan's bill. So the reduced bill will be the original bill minus the $12 dessert.
Let's substitute the variables and write the equation:
Reduced Bill = Original Bill - $12 (equation 1)
Next, we know that the tip was 20% of the reduced bill and it amounted to $15. So, we can set up another equation:
$15 = 0.20 * Reduced Bill (equation 2)
Now, let's substitute the value of the reduced bill from equation 1 into equation 2:
$15 = 0.20 * (Original Bill - $12)
To finalize the equation, we can distribute the 0.20:
$15 = 0.20 * Original Bill - 0.20 * $12
This simplifies to:
$15 = 0.20 * Original Bill - $2.40 (equation 3)
Thus, the equation that will determine the amount of the original bill, b, is:
$15 = 0.20 * b - $2.40