A hotel manager found that his gross receipts for the day, including a 9% sales tax, were $3927.27 . Find the amount of sales tax collected

109% ---> 3927.27

1% ----> 3927.27/109

9% = 9(3927.27/109)
= ...

To find the amount of sales tax collected, we need to first determine the total amount of gross receipts before the sales tax was included.

Let's assume x represents the total amount of gross receipts before the sales tax.

Now, we know that the sales tax rate is 9%, which means the sales tax collected is 9% of the gross receipts before the tax.

Mathematically, we can represent this as:

Sales Tax = 9% of Gross Receipts before Tax
Sales Tax = 0.09 * x

Now, let's calculate the total amount of gross receipts after the tax:

Total Gross Receipts = Gross Receipts before Tax + Sales Tax
Total Gross Receipts = x + 0.09 * x
Total Gross Receipts = 1.09 * x

We are given that the total gross receipts after including the sales tax is $3927.27. Therefore, we can set up the equation:

3927.27 = 1.09 * x

To solve for x, we can divide both sides of the equation by 1.09:

3927.27 / 1.09 = x

Simplifying this, we find:

x ≈ 3600.25

Therefore, the total amount of gross receipts before the sales tax was approximately $3600.25.

To find the amount of sales tax collected, we can subtract the gross receipts before the tax from the total gross receipts:

Sales Tax Collected = Total Gross Receipts - Gross Receipts before Tax
Sales Tax Collected = 3927.27 - 3600.25
Sales Tax Collected ≈ 327.02

Hence, the amount of sales tax collected is approximately $327.02.