To understand which term represents the cost of the shoes after the discount, let's break down the expression given in the problem step-by-step.
We start with:
[tex]\[ c + (1 - 0.15)s + 0.09[c + (1 - 0.15)s] \][/tex]
1. Identify the discount term:
The store offers a 15% discount on all shoes. The original cost of the shoes is denoted by [tex]\( s \)[/tex]. A 15% discount means Ayla will pay 85% of the original cost. So, the expression representing the cost after the discount is:
[tex]\[ (1 - 0.15)s \][/tex]
This simplifies to:
[tex]\[ 0.85s \][/tex]
2. Identify the parts of the given expression:
- The term [tex]\( c \)[/tex] represents the cost of clothes (which is not affected by the discount).
- The term [tex]\( (1 - 0.15)s \)[/tex] represents the cost of the shoes after the 15% discount.
- The term [tex]\( 0.09[c + (1 - 0.15)s] \)[/tex] represents the 9% sales tax applied to the total cost of clothes and the discounted shoes.
Now, we need to identify which term specifically represents the cost of the shoes after the discount.
From the options:
A. [tex]\( [c + (1 - 0.15)s] \)[/tex]
This expression includes both the cost of clothes and the discounted cost of the shoes, so it does not represent just the shoes' cost.
B. [tex]\( (1 - 0.15) \)[/tex]
This expression represents the discount factor but not the cost of the shoes since it does not include [tex]\( s \)[/tex].
C. [tex]\( 0.09[c + (1 - 0.15)s] \)[/tex]
This expression represents the sales tax on the total cost, not just the shoes.
D. [tex]\( (1 - 0.15)s \)[/tex]
This expression correctly represents the cost of the shoes after applying the 15% discount.
Thus, the correct term that represents the cost of the shoes after the discount is:
[tex]\[ (1 - 0.15)s \][/tex]
Hence, the correct answer is:
[tex]\[ \text{D. } (1-0.15)s \][/tex]
