Question

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:
\[
\boxed{1.2816xx}
\]