Question

Adam goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Adam decides to leave a tip of 21% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Adam paid.

Answer 1

To find the total amount that Adam paid, we start by calculating the tax and the tip based on the subtotal \( xx \).

1. **Calculate the tax:**
The tax is 5% of the subtotal \( xx \). So, the amount of tax can be calculated as:
\[
\text{Tax} = 0.05 \times xx
\]

2. **Calculate the total bill including tax:**
The total bill after tax is:
\[
\text{Total Bill} = xx + \text{Tax} = xx + 0.05xx = 1.05xx
\]

3. **Calculate the tip on the entire bill:**
The tip is 21% of this total bill. Therefore, the amount of tip is:
\[
\text{Tip} = 0.21 \times (1.05xx)
\]

4. **Calculate the total amount paid:**
The total amount Adam paid is the sum of the total bill and the tip. So:
\[
\text{Total Amount Paid} = \text{Total Bill} + \text{Tip}
\]
Substituting the expressions we derived:
\[
\text{Total Amount Paid} = 1.05xx + 0.21 \times (1.05xx)
\]

5. **Simplifying the expression:**
\[
\text{Total Amount Paid} = 1.05xx + 0.21 \times 1.05xx = 1.05xx + 0.2205xx = (1.05 + 0.2205)xx = 1.2705xx
\]

Thus, the expression representing the total amount that Adam paid is:
\[
\text{Total Amount Paid} = 1.2705xx
\]