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Sam is shopping for clothes. There's a $9 \%$ sales tax where he lives. Select the expression that gives the price of clothes after including the sales tax, where $c$ is the original cost of the clothes.
$1.9 c$
1.09 c
$1 c+0.9 c$
$1.09 c+0.09 c$
Answer (2)
Calculate the sales tax amount: 0.09 c
Add the sales tax to the original cost: c + 0.09 c
Simplify the expression: ( 1 + 0.09 ) c = 1.09 c
The final expression for the price after tax is 1.09 c
Explanation
Problem Analysis Let's analyze the problem. We need to find the expression that represents the total price of clothes after adding a 9% sales tax to the original cost, denoted by 'c'.
Calculating Sales Tax The sales tax amount is calculated by multiplying the original cost 'c' by the sales tax rate, which is 9% or 0.09. So, the sales tax amount is 0.09c.
Finding Total Price To find the total price, we add the sales tax amount to the original cost: c + 0.09c.
Simplifying the Expression We can factor out 'c' from the expression: (1 + 0.09)c = 1.09c.
Final Answer Therefore, the expression that gives the price of clothes after including the sales tax is 1.09c.
Examples
Imagine you are buying a shirt that costs $20. With a 9% sales tax, you would multiply $20 by 0.09 to find the tax amount, which is $1.80. Then, you add the tax to the original price: $20 + $1.80 = $21.80. This is the same as multiplying the original price by 1.09: $20 * 1.09 = $21.80. This calculation is useful in everyday shopping to quickly estimate the total cost of items.
The total price of clothes after adding a 9% sales tax is represented by the expression 1.09 c . This is calculated by adding the sales tax amount, 0.09 c , to the original cost, c , and simplifying the expression. Thus, the correct choice is the option 1.09 c .
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