Final answer:
Dan's monthly internet fee before taxes is $50.00. By subtracting the installation fee from the total paid and then dividing by the total number of months and correcting for tax, we arrive at the base monthly fee.
Step-by-step explanation:
To calculate Dan's monthly fee before taxes, we need to first find out the total amount spent on the monthly service alone. We know that Dan has paid a total of $365.96 after 4 months, which includes a one-time installation fee of $150 and the tax on the monthly fee over the 4 months.
To find the total amount paid for the service, we subtract the installation fee from the total amount paid:
Total amount paid for service = $365.96 - $150 = $215.96
Since the monthly fee is subject to an 8% tax, we can set up an equation where the monthly fee before tax is represented as 'x'. The total amount for 4 months after adding the tax would be 4x * 1.08 (because 8% of x is 0.08x, so the total with tax is x + 0.08x = 1.08x for one month).
4 * 1.08x = $215.96
Solving for x gives:
x = $215.96 / (4 * 1.08) = $50
Therefore, Dan's monthly fee before taxes is $50.00.