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A store is offering [tex]\(20\% \)[/tex] off all shoes. Rosalie purchases shoes and clothes. The expression representing her total cost (including [tex]\(7\%\)[/tex] tax) is [tex]\(c+(1-0.2)s+0.07[c+(1-0.2)s]\)[/tex]. Which term represents the cost of the shoes after the discount?

A. [tex]\((1-0.2)s\)[/tex]

B. [tex]\(0.07[c+(1-0.2)s]\)[/tex]

C. [tex]\((1-0.2)\)[/tex]

D. [tex]\([c+(1-0.2)s]\)[/tex]

Sagot :

GinnyAnsweridn
To determine which term represents the cost of the shoes after the discount, let's break down the given expression and understand each part:

The total cost expression is:
[tex]\[ c + (1 - 0.2)s + 0.07[c + (1 - 0.2)s] \][/tex]

Here, [tex]\(c\)[/tex] represents the cost of the clothes Rosalie purchases, and [tex]\(s\)[/tex] represents the original cost of the shoes.

1. Initial Cost of Shoes
- The original cost of the shoes is [tex]\(s\)[/tex].

2. Discount on the Shoes
- The store offers a [tex]\(20\%\)[/tex] discount, which is calculated as [tex]\(0.2 \times s\)[/tex].
- Therefore, the discount amount is [tex]\(0.2s\)[/tex].

3. Cost of Shoes After Discount
- To find the cost after the discount, subtract the discount from the original cost:
[tex]\[ s - 0.2s = (1 - 0.2)s \][/tex]

So, the term [tex]\((1-0.2)s\)[/tex] accurately represents the cost of the shoes after applying the [tex]\(20\%\)[/tex] discount.

Therefore, among the given choices, the term that represents the cost of the shoes after the discount is:

A. [tex]\((1-0.2)s\)[/tex]
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