Ana is purchasing new furniture and must pay a 10% sales tax. She can have the furniture delivered for an additional $25 fee that is not taxed. Which function represents the amount Ana will pay for furniture with a pretax price of $x$ dollars?
A. [tex]$P(x)=0.10 x+25$[/tex]
B. [tex]$P(x)=0.10(x+25)$[/tex]
C. [tex]$P(x)=1.10 x+25$[/tex]
D. [tex]$P(x)=1.10(x+25)$[/tex]
Answer (2)
Calculate the sales tax: 0.10 x .
Add the sales tax to the pretax price: x + 0.10 x = 1.10 x .
Add the delivery fee: 1.10 x + 25 .
The total amount Ana will pay is P ( x ) = 1.10 x + 25 .
Explanation
Problem Analysis Let's analyze the problem. Ana is buying furniture with a pretax price of x dollars. There's a 10% sales tax on the furniture and a fixed delivery fee of 25 t ha t i s n o tt a x e d . W e n ee d t o f in d a f u n c t i o n P(x)$ that represents the total amount Ana will pay.
Calculating Sales Tax First, we calculate the sales tax on the furniture. The sales tax is 10% of the pretax price x , which can be written as 0.10 x .
Calculating Subtotal Next, we add the sales tax to the pretax price to find the subtotal. This is x + 0.10 x , which simplifies to 1.10 x .
Calculating Total Amount Finally, we add the delivery fee of $25 to the subtotal. The total amount Ana will pay is 1.10 x + 25 . Therefore, the function that represents the total amount is P ( x ) = 1.10 x + 25 .
Final Answer The function that represents the amount Ana will pay for furniture with a pretax price of x dollars is P ( x ) = 1.10 x + 25 .
Examples
Imagine you're buying a couch online for $500 before tax. With a 10% sales tax, the couch costs an additional $50 in tax. If the website charges a $25 delivery fee, the total cost would be $500 + $50 + $25 = $575. This function helps you quickly calculate the total cost for any furniture price, including tax and delivery.
The function that represents the total amount Ana will pay for her furniture is P ( x ) = 1.10 x + 25 . This includes the 10% sales tax on the furniture and a $25 delivery fee. Therefore, the correct answer is option C.
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