Select the correct answer. A furniture store is having a weekend sale and is offering a \( 20 \% \) discount on patio chairs and tables. The sales tax on furniture is \( 6.25 \% \). Using function composition, how can you represent the total amount, \( A \), that you would need to pay for furniture that costs \( x \) dollars? A. \( A(x)=0.735 x \) B. \( A(x)=0.75 x \) C. \( A(x)=0.85 x \) D. \( A(x)=1.25 x \)

To find the total amount \( A \) you would need to pay after the discount and adding the sales tax, we first calculate the price after the discount. A \( 20\% \) discount on the price \( x \) leaves you with \( 80\% \) of \( x \), which is represented as \( 0.8x \). Then, you add the \( 6.25\% \) sales tax to that amount. The total becomes: \[ A(x) = 0.8x + 0.0625(0.8x) = 0.8x(1 + 0.0625) = 0.8x(1.0625) = 0.85x. \] Therefore, the correct answer is option C: \( A(x) = 0.85x \). Now, let's talk about some interesting related insights! Did you know that sales and discounts have a rich history? The concept of offering discounts to lure customers dates back centuries, where merchants would lower prices during the off-season to clear out inventory. Today, it’s a staple of marketing strategy, especially during holidays, creating a win-win scenario for both consumers and retailers! When dealing with discounts and taxes, it’s easy to make simple mistakes in calculations. A common pitfall is forgetting to apply the discount before calculating the tax. Always remember: discounts come first! A neat trick is to break down calculations into steps and double-check each stage to ensure accuracy. Happy shopping!