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Chapter 3: Problem 2

A beverage store charges a base price of \(x\) dollars for one keg of root beer. A sales tax of a certain percentage is applied to the base price, and an untaxed deposit for the keg is added. If the total amount, in dollars, paid at the time of purchase for one keg is given by the expression \(1.07 x+17\), then what is the sales tax, expressed as a percentage of the base price? A) \(0.07 \%\) B) \(1.07 \%\) C) \(7 \%\) D) \(17 \%\)

Short Answer

Expert verified
The sales tax percentage is 7%. Answer: \(\textbf{(C) } 7\%\).

Step by step solution

01

Identify the sales tax and the deposit

From the expression \(1.07x + 17\), we can identify that 1.07x represents the base price after applying the sales tax and 17 represents the deposit.
02

Extract the sales tax factor

Since the expression \(1.07x\) represents the price after sales tax is applied, we can determine the sales tax factor by noticing that the base price \(x\) is multiplied by 1.07. This means the sales tax factor is \((1.07-1)\).
03

Convert the tax factor to percentage

The sales tax factor is the multiplicative effect of the sales tax on the base price, and it's expressed as decimal value (in this case, \((1.07 - 1)\)). To convert it to a percentage, we simply multiply the value by 100. Sales tax percentage = \((1.07 - 1) * 100\).
04

Calculate the sales tax percentage

Now that we have the expression for the sales tax percentage, we can calculate it by using the formula: Sales tax percentage = \((1.07 - 1) * 100 = 0.07 * 100 = 7\%\)
05

Choose the correct answer

Since the sales tax is calculated to be 7%, the correct answer is: C) \(7 \%\)

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