Ian goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 8% is applied to the bill. Ian decides to leave a tip of 18% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Ian paid.

Answer 1

Let's break down the calculation step-by-step:

1. Subtotal (Bill amount): \( xx \)

2. Tax (8% of the subtotal): \[ \text{Tax} = 0.08 \times xx \]

3. Total after tax: \[ \text{Total after tax} = xx + (0.08 \times xx) = xx(1 + 0.08) = xx \times 1.08 \]

4. Tip (18% of the total after tax): \[ \text{Tip} = 0.18 \times (xx \times 1.08) \]

5. Total amount paid by Ian: This is the sum of the total after tax and the tip: \[ \text{Total amount paid} = \text{Total after tax} + \text{Tip} \] Substituting the expressions we calculated: \[ \text{Total amount paid} = (xx \times 1.08) + (0.18 \times (xx \times 1.08)) \]

6. Factor out \( xx \times 1.08 \): \[ \text{Total amount paid} = (xx \times 1.08) \times (1 + 0.18) = (xx \times 1.08) \times 1.18 \]

7. Therefore, the final expression for the total amount Ian paid is: \[ \text{Total amount paid} = xx \times 1.08 \times 1.18 \]

8. Simplifying \( 1.08 \times 1.18 \): \[ 1.08 \times 1.18 = 1.2724 \]

So, the total amount that Ian paid can be expressed as: \[ \text{Total amount paid} = xx \times 1.2724 \]