Lydia goes to a restaurant and the subtotal on the bill was $x$ dollars. A tax of $6 \%$ is applied to the bill. Lydia decides to leave a tip of $23 \%$ on the entire bill (including the tax). Write an expression in terms of $x$ that represents the total amount that Lydia paid. $\newline$ Answer:

Full solution

Q. Lydia goes to a restaurant and the subtotal on the bill was

x

dollars. A tax of

6 \%

is applied to the bill. Lydia decides to leave a tip of

23 \%

on the entire bill (including the tax). Write an expression in terms of

x

that represents the total amount that Lydia paid.

\newline

Answer:

Calculate Tax: First, calculate the tax on the subtotal of the bill. $\newline$ Tax = Subtotal * Tax rate $\newline$ Tax = $x * 6\%$ $\newline$ Tax = $x * 0.06$
Add to Subtotal: Next, add the tax to the subtotal to get the total bill before the tip. $\newline$ Total before tip = Subtotal + Tax $\newline$ Total before tip = $x + x \times 0.06$ $\newline$ Total before tip = $x \times (1 + 0.06)$ $\newline$ Total before tip = $x \times 1.06$
Calculate Tip: Now, calculate the tip based on the total bill including tax. $\newline$ Tip $= \text{Total before tip} \times \text{Tip percentage}$ $\newline$ Tip $= x \times 1.06 \times 23\%$ $\newline$ Tip $= x \times 1.06 \times 0.23$
Find Total Amount Paid: Finally, add the tip to the total before tip to find the total amount Lydia paid. $\newline$ Total amount paid = Total before tip + Tip $\newline$ Total amount paid = $x \times 1.06 + x \times 1.06 \times 0.23$ $\newline$ Total amount paid = $x \times 1.06 \times (1 + 0.23)$ $\newline$ Total amount paid = $x \times 1.06 \times 1.23$