To identify the term that represents the cost of the shoes after the discount, let's analyze the given expression and what each part represents.
Given Expression:
[tex]\[ c + (1 - 0.25)s + 0.08[c + (1 - 0.25)s] \][/tex]
- [tex]\( c \)[/tex] represents the cost of the clothes before tax.
- [tex]\( 1 - 0.25 \)[/tex] represents the fraction of the original price remaining after applying the 25% discount on the shoes.
- [tex]\( (1 - 0.25)s \)[/tex] represents the cost of the shoes after applying the 25% discount.
- [tex]\( 0.08 \)[/tex] is the tax rate (8%).
- [tex]\( 0.08[c + (1 - 0.25)s] \)[/tex] represents the tax applied to the total cost of clothes and discounted shoes.
Now, we are asked to identify the term that represents the cost of the shoes after the discount. Upon examining the parts of the expression:
Choice A: [tex]\( [c + (1 - 0.25)s] \)[/tex]
- This term includes the cost of clothes and the discounted cost of the shoes, but it is not specifically isolating the cost of the shoes alone after the discount. So, it is not the correct answer.
Choice B: [tex]\( (1 - 0.25) \)[/tex]
- This term represents the fraction of the price of the shoes that remains after the discount but does not include the price of the shoes [tex]\( s \)[/tex]. Thus, it is not the correct answer.
Choice C: [tex]\( 0.08[c + (1 - 0.25)s] \)[/tex]
- This term represents the tax on the total purchase (clothes and discounted shoes). Therefore, it is not the correct answer.
Choice D: [tex]\( (1 - 0.25)s \)[/tex]
- This term specifically represents the price of the shoes [tex]\( s \)[/tex] after applying the 25% discount. This is exactly what we are looking for.
Therefore, the correct answer is:
[tex]\[ \text{D. } (1 - 0.25)s \][/tex]
