Question

Samuel goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 8% is applied to the bill. Samuel 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 Samuel paid.

Answer 1

Samuel paid a total of xx(1.2744), which includes the subtotal xx, tax at 8% (0.08xx), and a tip at 18% on the entire bill after tax (0.18 × 1.08xx).

Step-by-step explanation:

To calculate the total amount Samuel paid, we need to include both tax and tip in our calculation. The subtotal of the bill is represented as xx dollars. We first calculate the tax by multiplying the subtotal by the tax rate (8%), which is 0.08 in decimal form. Thus, the tax amount is 0.08xx. The bill including tax is now xx + 0.08xx.

Next, we calculate the tip. The tip is 18% of the entire bill (including tax), so we first need to find the total bill after tax, which we have from the previous step (1.08xx). We then convert 18% to a decimal, which is 0.18, and multiply it by 1.08xx to find the tip amount.0.18 × 1.08xx.

The total amount Samuel pays is the sum of the original bill, the tax, and the tip. So, we add the subtotal, the tax, and the tip together resulting in xx + 0.08xx + (0.18 × 1.08xx). Simplifying this, we get:

xx(1 + 0.08 + (0.18 × 1.08)), which simplifies to xx(1.08 + 0.1944), and finally, xx(1.2744). This is the expression for the total amount Samuel paid in terms of xx.