Heather Paid $ 2 , 022.30 \$2,022.30 $2 , 022.30 For A Computer. If The Price Paid Includes A 7 % 7\% 7% Sales Tax, Which Of The Following Equations Can Be Used To Determine The Price Of The Computer After Tax?(Let X X X Represent The Cost Of The Computer

When purchasing an item, the total price paid often includes a sales tax, which is a percentage of the original price. In this scenario, Heather paid $$2,022.30$ for a computer, and the price includes a $7$ sales tax. To determine the original price of the computer before tax, we need to establish a mathematical relationship between the sales tax and the original price.

The Role of Sales Tax in Pricing

Sales tax is a percentage of the original price, and it is added to the original price to determine the total price paid. In this case, the sales tax is $7\%$, which means that $7\%$ of the original price is added to the original price to get the total price paid.

Mathematical Representation of Sales Tax

Let $x$ represent the cost of the computer before tax. The sales tax is $7\%$ of the original price, which can be represented as $0.07x$. The total price paid, including the sales tax, is $\$2,022.30$. We can set up an equation to represent this relationship:

$$x + 0.07x = 2022.30$$

Simplifying the Equation

To simplify the equation, we can combine like terms:

$$1.07x = 2022.30$$

Solving for x

To solve for $x$, we can divide both sides of the equation by $1.07$:

$$x = \frac{2022.30}{1.07}$$

Calculating the Original Price

Now that we have the equation, we can calculate the original price of the computer before tax:

$$x = \frac{2022.30}{1.07} = 1885.13$$

Conclusion

In this scenario, the equation $1.07x = 2022.30$ can be used to determine the price of the computer after tax. By simplifying the equation and solving for $x$, we can calculate the original price of the computer before tax.

Key Takeaways

• The sales tax is $7\%$ of the original price.
• The total price paid, including the sales tax, is $\$2,022.30$.
• The equation $1.07x = 2022.30$ can be used to determine the price of the computer after tax.
• By simplifying the equation and solving for $x$, we can calculate the original price of the computer before tax.

Real-World Applications

Understanding the relationship between sales tax and original price is essential in real-world applications, such as:

• Calculating the total cost of a purchase, including sales tax.
• Determining the original price of an item before tax.
• Comparing prices of similar items, including sales tax.

Q: What is the formula to calculate the original price of an item before tax?

A: The formula to calculate the original price of an item before tax is:

$$x = \frac{Total\ Price\ Paid}{1 + Sales\ Tax\ Rate}$$

Where $x$ is the original price, $Total\ Price\ Paid$ is the total price paid, including sales tax, and $Sales\ Tax\ Rate$ is the sales tax rate as a decimal.

Q: How do I calculate the sales tax rate as a decimal?

A: To calculate the sales tax rate as a decimal, you need to divide the sales tax rate by 100. For example, if the sales tax rate is 7%, you would divide 7 by 100 to get 0.07.

Q: What if I don't know the sales tax rate?

A: If you don't know the sales tax rate, you can use the following formula to calculate the sales tax rate:

$$Sales\ Tax\ Rate = \frac{Total\ Price\ Paid - Original\ Price}{Original\ Price}$$

Q: How do I calculate the total price paid, including sales tax?

A: To calculate the total price paid, including sales tax, you need to multiply the original price by the sales tax rate and add the result to the original price.

Q: What if I want to calculate the sales tax amount separately?

A: To calculate the sales tax amount separately, you can use the following formula:

$$Sales\ Tax\ Amount = Total\ Price\ Paid - Original\ Price$$

Q: Can I use a calculator to calculate the original price and sales tax amount?

A: Yes, you can use a calculator to calculate the original price and sales tax amount. Simply enter the total price paid and sales tax rate, and the calculator will do the rest.

Q: Are there any online tools or calculators that can help me calculate the original price and sales tax amount?

A: Yes, there are many online tools and calculators available that can help you calculate the original price and sales tax amount. Some popular options include:

• Online calculators, such as Google Calculator or Microsoft Calculator
• Sales tax calculators, such as TaxJar or SalesTaxCalculator
• Online price comparison tools, such as PriceGrabber or NexTag

Q: Can I use this formula to calculate the original price and sales tax amount for multiple items?

A: Yes, you can use this formula to calculate the original price and sales tax amount for multiple items. Simply repeat the calculation for each item, using the total price paid and sales tax rate for each item.

Q: Are there any assumptions or limitations to this formula?

A: Yes, there are some assumptions and limitations to this formula. For example:

• This formula assumes that the sales tax rate is a fixed percentage of the original price.
• This formula assumes that the sales tax rate is applied to the original price, not to the total price paid.
• This formula may not be accurate if the sales tax rate changes over time or if there are other taxes or fees applied to the purchase.

Q: Can I use this formula to calculate the original price and sales tax amount for items with different sales tax rates?

A: Yes, you can use this formula to calculate the original price and sales tax amount for items with different sales tax rates. Simply repeat the calculation for each item, using the total price paid and sales tax rate for each item.

Q: Are there any other formulas or calculations that I can use to calculate the original price and sales tax amount?

A: Yes, there are other formulas and calculations that you can use to calculate the original price and sales tax amount. Some popular options include:

• The formula for calculating the original price and sales tax amount using the total price paid and sales tax rate: $x = \frac{Total\ Price\ Paid}{1 + Sales\ Tax\ Rate}$
• The formula for calculating the sales tax amount using the total price paid and original price: $Sales\ Tax\ Amount = Total\ Price\ Paid - Original\ Price$
• The formula for calculating the sales tax rate using the total price paid and original price: $Sales\ Tax\ Rate = \frac{Total\ Price\ Paid - Original\ Price}{Original\ Price}$