Final answer:
The restaurant charged $15.56 for lunch excluding tax, and the sales tax amounted to $1.24. This can be determined by dividing the total paid ($16.80) by 1.08 to get the price before tax, then multiplying that amount by the tax rate (0.08) to find the sales tax.
Step-by-step explanation:
To calculate how much the restaurant charged for lunch excluding tax, and how much sales tax was charged, we should first determine the total percentage of the sale that represents both the cost of lunch and sales tax combined. Since the sales tax is 8%, the total percentage representing the cost of lunch and sales tax is 100% + 8% = 108%.
To find the original price before the tax, we will need to divide the total amount paid by 1.08 (since 108% as a decimal is 1.08). Using the total amount paid of $16.80, we get:
Original price before tax = Total amount paid / 1.08 = $16.80 / 1.08 = $15.56.
Now to find out the amount of sales tax, we multiply the cost before tax by the tax rate (as a decimal):
Sales tax = Original price before tax x Sales tax rate = $15.56 x 0.08 = $1.24. So, the amount charged by the restaurant for lunch is $15.56 and the sales tax owed is $1.24.
The correct answer to the multiple choice question provided by the student is option B: $15.56 for lunch and $1.24 for sales tax.