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: \[ \text{Total amount paid} = 1.06 * 1.15 * xx \]