Deondra goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 8% is applied to the bill. Deondra decides to leave a tip of 23% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Deondra paid.

Answer 1

To find the total amount that Deondra paid, we need to account for both the tax and the tip.

1. Calculate the tax: The tax is 8% of the subtotal \(xx\). This can be expressed as: \[ \text{Tax} = 0.08 \cdot xx \]

2. Calculate the total bill with tax: The total bill after tax is the subtotal plus the tax: \[ \text{Total with tax} = xx + 0.08 \cdot xx = xx (1 + 0.08) = xx \cdot 1.08 \]

3. Calculate the tip: The tip is 23% of the total bill with tax. This can be expressed as: \[ \text{Tip} = 0.23 \cdot (xx \cdot 1.08) \]

4. Calculate the total amount paid: The total amount Deondra paid is the total bill with tax plus the tip: \[ \text{Total amount paid} = \text{Total with tax} + \text{Tip} \] Substituting in the expressions we derived: \[ \text{Total amount paid} = (xx \cdot 1.08) + (0.23 \cdot (xx \cdot 1.08)) \]

5. Factor out \(xx \cdot 1.08\): \[ \text{Total amount paid} = xx \cdot 1.08 \cdot (1 + 0.23) \] This simplifies to: \[ \text{Total amount paid} = xx \cdot 1.08 \cdot 1.23 \]

Therefore, the expression that represents the total amount that Deondra paid is: \[ \text{Total amount paid} = xx \cdot 1.08 \cdot 1.23 \]