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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.
Answer:

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

Full solution

Q. Lydia goes to a restaurant and the subtotal on the bill was x x dollars. A tax of 6% 6 \% is applied to the bill. Lydia decides to leave a tip of 23% 23 \% on the entire bill (including the tax). Write an expression in terms of x x that represents the total amount that Lydia paid.\newlineAnswer:
  1. Calculate Tax: First, calculate the tax on the subtotal of the bill.\newlineTax = Subtotal * Tax rate\newlineTax = x6%x * 6\%\newlineTax = x0.06x * 0.06
  2. Add to Subtotal: Next, add the tax to the subtotal to get the total bill before the tip.\newlineTotal before tip = Subtotal + Tax\newlineTotal before tip = x+x×0.06x + x \times 0.06\newlineTotal before tip = x×(1+0.06)x \times (1 + 0.06)\newlineTotal before tip = x×1.06x \times 1.06
  3. Calculate Tip: Now, calculate the tip based on the total bill including tax. \newlineTip =Total before tip×Tip percentage= \text{Total before tip} \times \text{Tip percentage}\newlineTip =x×1.06×23%= x \times 1.06 \times 23\%\newlineTip =x×1.06×0.23= x \times 1.06 \times 0.23
  4. Find Total Amount Paid: Finally, add the tip to the total before tip to find the total amount Lydia paid.\newlineTotal amount paid = Total before tip + Tip\newlineTotal amount paid = x×1.06+x×1.06×0.23x \times 1.06 + x \times 1.06 \times 0.23\newlineTotal amount paid = x×1.06×(1+0.23)x \times 1.06 \times (1 + 0.23)\newlineTotal amount paid = x×1.06×1.23x \times 1.06 \times 1.23

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