Question

Brandon goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 6% is applied to the bill. Brandon decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Brandon paid.

Answer 1

To find the total amount that Brandon paid, we can break down the calculations step by step:

1. **Calculate the tax**: The tax is 6% of the subtotal (xx dollars).
- Tax = 0.06 * xx

2. **Calculate the total bill including tax**: This is the subtotal plus the tax.
- Total after tax = xx + 0.06 * xx = xx(1 + 0.06) = xx * 1.06

3. **Calculate the tip**: The tip is 15% of the total amount after tax.
- Tip = 0.15 * (Total after tax) = 0.15 * (xx * 1.06)

4. **Calculate the total amount paid**: The total amount paid is the total after tax plus the tip.
- Total amount paid = Total after tax + Tip
- Total amount paid = (xx * 1.06) + (0.15 * (xx * 1.06))

Now we can factor out the common term:

Total amount paid = xx * 1.06 + 0.15 * xx * 1.06
= xx * 1.06 (1 + 0.15)
= xx * 1.06 * 1.15

Finally, the expression representing the total amount that Brandon paid is:
\[
\text{Total amount paid} = xx * 1.06 * 1.15
\]

Calculating \(1.06 * 1.15\) gives approximately \(1.221\), so you could simplify this to:
\[
\text{Total amount paid} \approx 1.221 * xx
\]

However, keeping it in the exact form using the products is clearer:
\[
\text{Total amount paid} = 1.06 * 1.15 * xx
\]