Question

Adrian goes to a store and buys an item that costs xx dollars. He has a coupon for 40% off, and then a 7% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Adrian paid at the register.

Answer 1

To find the total amount that Adrian paid at the register after applying the coupon discount and adding the tax, we can follow these steps:

1. **Calculate the 40% discount** on the item priced at \( x \) dollars:
\[
\text{Discount amount} = 0.40 \times x = 0.4x
\]
Thus, the price after the discount is:
\[
\text{Discounted price} = x - 0.4x = 0.6x
\]

2. **Calculate the 7% tax** on the discounted price:
\[
\text{Tax amount} = 0.07 \times (0.6x) = 0.07 \cdot 0.6x = 0.042x
\]

3. **Add the tax to the discounted price** to get the total amount paid at the register:
\[
\text{Total amount} = \text{Discounted price} + \text{Tax amount} = 0.6x + 0.042x
\]
Combining these gives:
\[
\text{Total amount} = (0.6 + 0.042)x = 0.642x
\]

Thus, the expression that represents the total amount that Adrian paid at the register is:
\[
\boxed{0.642x}
\]