The cash register total including sales taxes is $46,830, and the sales tax rate is 5%. What is the
The correct answer and explanation is :
To find the original price of an item before sales tax is applied, we need to use the following formula:
$$
\text{Original Price} = \frac{\text{Total Price}}{1 + \text{Sales Tax Rate}}
$$
Where:
- Total Price is the price after the sales tax is added (in this case, \$46,830).
- Sales Tax Rate is 5%, or 0.05 in decimal form.
Step 1: Identify the known values
- Total Price = \$46,830
- Sales Tax Rate = 5% = 0.05
Step 2: Substitute the values into the formula
$$
\text{Original Price} = \frac{46,830}{1 + 0.05} = \frac{46,830}{1.05}
$$
Step 3: Perform the calculation
$$
\text{Original Price} = \frac{46,830}{1.05} = 44,600
$$
Step 4: Interpret the result
The original price of the item, before sales tax, is \$44,600.
Explanation
The total amount you see at the register includes both the original price of the goods and the sales tax. The sales tax rate is applied to the original price, and this amount is then added to the total price. Since we are given the total price after tax, we can reverse this process to find the original price by dividing the total by 1 plus the tax rate. In this case, we used a tax rate of 5% (or 0.05), which means the total price is 105% of the original price.
By dividing \$46,830 by 1.05, we remove the 5% sales tax and find the original price of \$44,600. This method works because 105% of the original price is equal to the total price after tax, and dividing by 1.05 effectively isolates the portion that was the original price before tax.
Understanding this process is crucial when working with sales tax in real-world scenarios, as it allows you to backtrack from the total price to the original amount before tax was added.