A store is offering $15 \% off all shoes. Ayla purchases shoes and clothes. The expression representing her total cost (including 9\% tax) is $c+(1-0.15) s+0.09[c+(1-0.15) s]$. Which term represents the cost of the shoes after the discount?
A. $(1-0.15) s$
B. $(1-0.15)$
C. $[c+(1-0.15) s]$
D. $0.09[c+(1-0.15) s]$
Answer (2)
The expression for the total cost is c + ( 1 − 0.15 ) s + 0.09 [ c + ( 1 − 0.15 ) s ] .
The term ( 1 − 0.15 ) s represents the cost of the shoes after a 15% discount.
The term c represents the cost of the clothes.
The term 0.09 [ c + ( 1 − 0.15 ) s ] represents the sales tax on the total cost.
The cost of the shoes after the discount is ( 1 − 0.15 ) s .
Explanation
Understanding the Problem The problem provides an expression for the total cost of Ayla's purchase, which includes clothes and shoes with a discount and sales tax. We need to identify the term that represents the cost of the shoes after the discount is applied but before tax.
Analyzing the Expression The given expression is c + ( 1 − 0.15 ) s + 0.09 [ c + ( 1 − 0.15 ) s ] .
c represents the cost of the clothes.
s represents the original cost of the shoes.
0.15 represents the discount rate on the shoes.
0.09 represents the sales tax rate.
Identifying the Discounted Shoe Cost The term ( 1 − 0.15 ) s represents the original price of the shoes, s , reduced by 15% . This is the discounted price of the shoes before tax is applied.
Understanding the Tax Term The term 0.09 [ c + ( 1 − 0.15 ) s ] represents the sales tax, which is 9% of the total cost of the clothes and the discounted shoes.
Final Answer Therefore, the term that represents the cost of the shoes after the discount is ( 1 − 0.15 ) s .
Examples
Understanding discounts is crucial in everyday shopping. For instance, if you want to buy a shirt that originally costs $25 and it's on sale for 20% off, you would calculate the discount as 0.20 × 25 = 5 , and the final price would be $25 - 5 = $20. This type of calculation helps you determine the actual savings and make informed purchasing decisions, whether you're buying clothes, electronics, or groceries.
The term that represents the cost of the shoes after the discount is ( 1 − 0.15 ) s . This shows the price of the shoes at 85% of their original price. Therefore, the correct answer is Option A: ( 1 − 0.15 ) s .
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