Answered

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A store is offering 20% off all shoes. Rosalie purchases shoes and clothes. The expression representing her total cost (including 7% 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]\(0.07[c + (1 - 0.2)s]\)[/tex]
B. [tex]\([c + (1 - 0.2)s]\)[/tex]
C. [tex]\((1 - 0.2)s\)[/tex]
D. [tex]\((1 - 0.2)\)[/tex]

Sagot :

GinnyAnswer
To determine which term represents the cost of the shoes after the discount from the given expression, let's carefully analyze the problem.

We know that Rosalie gets a 20% discount on the shoes. The original price of the shoes is denoted by [tex]\( s \)[/tex].

1. Calculate the discount on the shoes:

A 20% discount means Rosalie pays only 80% of the original price. We calculate this as follows:
[tex]\[ \text{Discounted price} = (1 - 0.2) \cdot s \][/tex]
Simplifying this:
[tex]\[ \text{Discounted price} = 0.8s \][/tex]

2. Analyze the expression:

The total cost expression given is:
[tex]\[ c + (1 - 0.2)s + 0.07[c + (1 - 0.2)s] \][/tex]
Here:
- [tex]\( c \)[/tex] is the cost of the clothes.
- [tex]\( (1-0.2)s \)[/tex] represents the price paid for the shoes after the discount.
- [tex]\( 0.07[c + (1-0.2)s] \)[/tex] represents the 7% tax on the total amount spent.

3. Identify the term for discounted shoes:

The term we are focused on is the one that directly calculates the cost of the shoes after the 20% discount, which is:
[tex]\[ (1-0.2)s \][/tex]

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

[tex]\[ \boxed{(1-0.2) s} \][/tex]

So, the correct answer is:
[tex]\[ \boxed{C. (1-0.2) s} \][/tex]
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