Question

Carter goes to a store and buys an item that costs xx dollars. He has a coupon for 5% off, and then a 6% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Carter paid at the register.

Answer 1

To find the total amount that Carter paid after applying the coupon and adding the tax, we can break down the calculations into two main steps:

1. **Applying the 5% Coupon**:
The item costs \( x \) dollars. With a 5% discount, the amount of the discount is \( 0.05x \). Therefore, the price after the discount is:
\[
x - 0.05x = 0.95x
\]

2. **Calculating the 6% Tax on the Discounted Price**:
After applying the discount, the price is \( 0.95x \). Now, we need to add 6% tax on this discounted price. The amount of tax is:
\[
0.06 \times 0.95x = 0.057x
\]
Thus, the total cost including tax is:
\[
0.95x + 0.057x = 1.007x
\]

Putting this all together, the total amount that Carter paid at the register can be expressed as:
\[
1.007x
\]

So, the final expression representing the total amount Carter paid in terms of \( x \) is:
\[
1.007x
\]