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: \[ \text{Total Amount Paid} = 1.2705xx \]