To solve this problem, let's break down the expression [tex]\( c + (1-0.25)s + 0.08[c + (1-0.25)s] \)[/tex].
1. Identifying Terms:
- [tex]\( c \)[/tex] represents the cost of the clothes.
- [tex]\( (1 - 0.25)s \)[/tex] represents the cost of the shoes after applying a 25% discount.
2. Discount Calculation:
- The term [tex]\( 0.25 \)[/tex] (or 25%) signifies the discount on the original shoe price [tex]\( s \)[/tex].
- Thus, [tex]\( (1 - 0.25) \)[/tex] represents the fraction of the shoe's cost that Declan needs to pay, which is [tex]\( 0.75 \)[/tex] or 75% of the original cost.
3. Cost After Discount:
- The product [tex]\( (1 - 0.25)s \)[/tex] specifically indicates the actual cost of the shoes after the discount is applied.
- Substituting the values gives us [tex]\( (0.75)s \)[/tex], showing the reduced price of the shoes.
4. Examining Given Options:
- Option A: [tex]\( (1-0.25) \)[/tex] – This term represents the fraction of the shoe's original cost that Declan needs to pay, not the actual cost after the discount.
- Option B: [tex]\( (1-0.25)s \)[/tex] – This term correctly represents the cost of the shoes after the discount.
- Option C: [tex]\( [c+(1-0.25)s] \)[/tex] – This term includes the cost of both clothes and shoes before tax is added.
- Option D: [tex]\( 0.08[c+(1-0.25)s] \)[/tex] – This term represents the 8% tax on both clothes and shoes after discount.
Thus, the term representing the cost of the shoes after the discount is clearly option B: [tex]\( (1-0.25)s \)[/tex].
The correct answer is B. [tex]\( (1-0.25)s \)[/tex].
