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A store is offering [tex]15\%[/tex] off all shoes. Ayla purchases shoes and clothes. The expression representing her total cost (including [tex]9\%[/tex] tax) is [tex]c+(1-0.15) s+0.09[c+(1-0.15) s][/tex].

Which term represents the cost of the shoes after the discount?



Answer :

GinnyAnswer
To determine which term represents the cost of the shoes after the discount in the given expression, let's break down and analyze the entire expression step-by-step:

[tex]\[ c + (1 - 0.15) s + 0.09 [ c + (1 - 0.15) s ] \][/tex]

1. Understand the Discount on Shoes:
- The original price of the shoes is denoted by [tex]\( s \)[/tex].
- The store is offering a 15% discount on the shoes.
- A 15% discount means Ayla pays only 85% of the original price.
- This can be represented as:
[tex]\[ 1 - 0.15 = 0.85 \][/tex]

2. Calculate the Discounted Price of Shoes:
- After the discount, the price of the shoes becomes:
[tex]\[ 0.85s \][/tex]

3. Total Cost Expression Explanation:
- [tex]\( c \)[/tex]: cost of the clothes (no discount is applied here).
- [tex]\( (1 - 0.15)s \)[/tex]: represents the cost of the shoes after the 15% discount, simplified to [tex]\( 0.85s \)[/tex].
- [tex]\( 0.09[c + (1 - 0.15)s] \)[/tex]: represents the 9% tax applied on the total cost of clothes and discounted shoes.

Putting this all together, we can see that the term [tex]\( (1 - 0.15)s \)[/tex] or more simplified as [tex]\( 0.85s \)[/tex], represents the cost of the shoes after the 15% discount.

Therefore, the term that represents the cost of the shoes after the discount is [tex]\( 0.85s \)[/tex].

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