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

Answer 1

To find the total amount that Elizabeth paid, we need to calculate the total bill including tax and tip.

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

2. Calculate the total bill including tax:
   The total bill including tax can be represented as:
   \[ \text{Total bill} = xx + \text{Tax} = xx + 0.06 \times xx = xx(1 + 0.06) = xx \times 1.06 \]

3. Calculate the tip:
   Elizabeth leaves a tip of 21% on the entire bill (which now includes tax).
   \[ \text{Tip} = 0.21 \times (\text{Total bill}) = 0.21 \times (xx \times 1.06) \]

4. Calculate the total amount paid:
   The total amount Elizabeth paid is the sum of the total bill and the tip.
   \[ \text{Total amount paid} = \text{Total bill} + \text{Tip} = (xx \times 1.06) + (0.21 \times (xx \times 1.06)) \]

   We can factor out \( xx \times 1.06 \) from the expression:
   \[ \text{Total amount paid} = xx \times 1.06 \times (1 + 0.21) \] \[ = xx \times 1.06 \times 1.21 \] \[ = xx \times (1.06 \times 1.21) \]

5. Calculate \( 1.06 \times 1.21 \):
   \[ 1.06 \times 1.21 = 1.2816 \]

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

Therefore, the final expression for the total amount Elizabeth paid in terms of \( xx \) is:
\[ \boxed{1.2816xx} \]