mrs. torres goes out of town on a business trip. she spends 3 nights in a hotel at a charge of $80 per…

mrs. torres goes out of town on a business trip. she spends 3 nights in a hotel at a charge of $80 per night. she pays 9% tax on the room and tips the maid service 10% of the room charge. mrs. torres also has meals worth $109.30 before tax and she tips 15%. if the total cost of her trip is $420.04, approximately what tax rate does mrs. torres pay on her meals?\na. 6%\nb. 7%\nc. 8%\nd. 9%

mrs. torres goes out of town on a business trip. she spends 3 nights in a hotel at a charge of $80 per night. she pays 9% tax on the room and tips the maid service 10% of the room charge. mrs. torres also has meals worth $109.30 before tax and she tips 15%. if the total cost of her trip is $420.04, approximately what tax rate does mrs. torres pay on her meals?\na. 6%\nb. 7%\nc. 8%\nd. 9%

Answer

Explanation:

Step1: Calculate room - related costs

The room charge per night is $80, and she stays for 3 nights, so the base - room cost is $80\times3 = 240$. The 9% tax on the room is $0.09\times240=21.6$, and the 10% tip to the maid service is $0.1\times240 = 24$. The total room - related cost is $240+21.6 + 24=285.6$.

Step2: Calculate meal - related costs

The cost of meals before tax is $109.30$, and the 15% tip on meals is $0.15\times109.30 = 16.395$. Let the tax rate on meals be $x$. The meal - related cost including tax and tip is $109.30(1 + x+0.15)=109.30(1.15 + x)$.

Step3: Set up the total - cost equation

The total cost of the trip is $420.04$. So, $285.6+109.30(1.15 + x)=420.04$. First, simplify the left - hand side: $285.6+109.30\times1.15+109.30x=420.04$. Calculate $109.30\times1.15 = 125.795$. Then the equation becomes $285.6+125.795+109.30x=420.04$. Combine like terms: $411.395+109.30x=420.04$.

Step4: Solve for $x$

Subtract $411.395$ from both sides: $109.30x=420.04 - 411.395=8.645$. Then $x=\frac{8.645}{109.30}\approx0.08$.

Answer:

c. 8%