Let's break down the components of the expression representing Declan's total cost, with each term explained step by step to identify the term representing the cost of the shoes after the discount.
The expression given is:
[tex]\[ c + (1 - 0.25) s + 0.08 [c + (1 - 0.25) s] \][/tex]
Here's the step-by-step breakdown:
1. Identifying the Variables:
- [tex]\( c \)[/tex]: Cost of the clothes.
- [tex]\( s \)[/tex]: Original cost of the shoes.
2. Discount on Shoes:
- The store offers a 25% discount on the shoes. Thus, the effective price of the shoes after this discount is given by:
[tex]\[
(1 - 0.25) s
\][/tex]
- Simplify this expression:
[tex]\[
(1 - 0.25) s = 0.75s
\][/tex]
- Therefore, [tex]\( 0.75s \)[/tex] represents the cost of the shoes after the discount.
3. Including 8% Tax:
- The tax of 8% ([tex]\(0.08\)[/tex]) applies to the total cost of clothes and discounted shoes.
- The expression for the total cost, including the tax, is:
[tex]\[
c + 0.75s + 0.08 [c + 0.75s]
\][/tex]
- Here, [tex]\(0.08 [c + 0.75s]\)[/tex] adds the 8% tax to the sum of the clothes and the discounted shoes.
Now that we have simplified the problem, let's address the specific question: Which term in the original expression represents the cost of the shoes after the discount?
From our breakdown, the term representing the cost of the shoes after the 25% discount is:
[tex]\[ 0.75s \][/tex]
Looking at the choices provided:
A. [tex]\[c + (1 - 0.25) s\][/tex]
B. [tex]\[(1 - 0.25) s\][/tex]
C. [tex]\[0.08 [c + (1 - 0.25) s]\][/tex]
D. [tex]\[(1 - 0.25)\][/tex]
The correct answer is:
B. [tex]\[(1 - 0.25) s\][/tex]
This simplifies to [tex]\(0.75s\)[/tex] and represents the cost of the shoes after applying the 25% discount.
