Nolan goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 6% is applied to the bill. Nolan 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 Nolan paid.

Answer 1

To find the total amount that Nolan paid, we can break it down into the following steps:

1. Calculate the tax: The tax is 6% of the subtotal \( xx \). This can be expressed as: \[ \text{Tax} = 0.06 \times xx \]

2. Calculate the total after tax: To find the total amount after adding the tax to the subtotal, we add the tax to the subtotal: \[ \text{Total after tax} = xx + (0.06 \times xx) = xx(1 + 0.06) = xx \times 1.06 \]

3. Calculate the tip: The tip is 21% of the total amount after tax. This can be expressed as: \[ \text{Tip} = 0.21 \times (xx \times 1.06) \]

4. Calculate the total amount paid: The total amount Nolan paid includes the total after tax plus the tip: \[ \text{Total amount paid} = \text{Total after tax} + \text{Tip} \] Substituting the expressions for total after tax and tip, we get: \[ \text{Total amount paid} = (xx \times 1.06) + (0.21 \times (xx \times 1.06)) \]

   Simplifying this, we can factor out \( xx \times 1.06 \): \[ \text{Total amount paid} = xx \times 1.06 \times (1 + 0.21) = xx \times 1.06 \times 1.21 \]

5. Final expression: Therefore, the expression for the total amount that Nolan paid in terms of \( xx \) is: \[ \text{Total amount paid} = xx \times 1.06 \times 1.21 \]

Calculating the multiplication: \[ 1.06 \times 1.21 = 1.2816 \]

Thus, the total amount that Nolan paid can also be expressed as: \[ \text{Total amount paid} = 1.2816 \times xx \]

This is the expression that represents the total amount Nolan paid in terms of \( xx \).