Question

Camila goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 7% is applied to the bill. Camila decides to leave a tip of 16% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Camila paid.

Answer 1

To find the total amount that Camila paid, we need to consider both the tax and the tip based on the subtotal \( xx \).

1. **Calculate the tax**:
The tax is 7% of the subtotal \( xx \). This can be expressed as:
\[
\text{Tax} = 0.07 \times xx
\]

2. **Calculate the total bill including tax**:
The total bill after adding the tax is:
\[
\text{Total with tax} = xx + \text{Tax} = xx + 0.07 \times xx
\]
This can be simplified as:
\[
\text{Total with tax} = xx (1 + 0.07) = 1.07 \times xx
\]

3. **Calculate the tip**:
Camila leaves a tip of 16% on the entire bill (which is the subtotal plus tax). The tip can be calculated as:
\[
\text{Tip} = 0.16 \times (1.07 \times xx) = 0.16 \times 1.07 \times xx
\]

4. **Calculate the total amount paid**:
Finally, the total amount Camila paid is the total with tax plus the tip:
\[
\text{Total amount paid} = \text{Total with tax} + \text{Tip}
\]
\[
= 1.07 \times xx + 0.16 \times 1.07 \times xx
\]
Factoring \( xx \) out, we get:
\[
= xx (1.07 + 0.16 \times 1.07)
\]
To simplify \( 1.07 + 0.16 \times 1.07 \), we calculate:
\[
0.16 \times 1.07 = 0.1712
\]
Therefore:
\[
1.07 + 0.1712 = 1.2412
\]

Now we have the final expression:
\[
\text{Total amount paid} = 1.2412 \times xx
\]

So, the expression that represents the total amount that Camila paid is:
\[
1.2412 \times xx
\]