To solve this problem, we need to identify the term that represents the cost of the shoes after a 20% discount.
Given the expression:
[tex]\[ c + (1 - 0.2)s + 0.07[c + (1 - 0.2)s] \][/tex]
First, let's break it down:
1. Initial cost of clothes: \( c \)
2. Initial cost of shoes before discount: \( s \)
3. Discount on shoes: 20%, which can be represented as \( 0.2 \times s \)
4. Cost of shoes after discount: We subtract the discount from the initial cost of the shoes. Since \( 1 - 0.2 = 0.8 \), the cost of the shoes after discount is \( 0.8s \).
5. Tax on the total cost: The total cost which needs to be taxed is \( c + 0.8s \). The tax rate is 7%, so the tax amount is \( 0.07 \times (c + 0.8s) \).
Now we focus on finding the term that represents the cost of the shoes after the discount. Considering the components of the given expression:
- \( c \): is the cost of the clothes.
- \( (1 - 0.2)s \): represents the cost of the shoes after the 20% discount.
Let's assess the choices:
- A. \( (1 - 0.2)s \): This term clearly shows the cost of the shoes after applying the 20% discount.
- B. \( 0.07[c + (1 - 0.2)s] \): This term represents the tax amount on the total cost.
- C. \( (1 - 0.2) \): This is just the discount factor (0.8), not the cost of the shoes after the discount.
- D. \( [c + (1 - 0.2)s] \): This represents the total cost of the clothes and the discounted shoes before tax.
The correct term representing the cost of the shoes after the discount is:
[tex]\[
\boxed{(1 - 0.2)s}
\][/tex]
Thus, the correct choice is:
[tex]\[
\boxed{A}
\][/tex]
