FAX machine purchased for 464.40 including tax.
Tax rate is 8%.
What is original price?
Is the answer 427.25?
Text book purchased for 158.60 including tax.
Tax rate is 9%
What is the original price?
Is the answer 412.98?
For #1, let x = the original price. Then the tax is 0.08x. Adding them together gives the total price of $464.40, so
x+0.08x = 464.40
solve for x. I get $430.00. Check my work. Checking it:
430.00 + 0.08*430 = 430.00 + 34.40 = 464.40.
#2 is worked the same way but I will let you do that. You should guess that your answer is not correct BECAUSE your original price is GREATER than the original price including the 9% tax. You can't add 9% of a number to that number and get a smaller number.
To find the original price, we need to subtract the tax amount from the total price.
For the FAX machine:
Tax rate = 8%
Total price = $464.40
1. Calculate the tax amount:
Tax amount = Total price * Tax rate / (100 + Tax rate)
Tax amount = $464.40 * 8 / (100 + 8)
Tax amount = $464.40 * 8 / 108
Tax amount = $464.40 * 0.0741
Tax amount = $34.39
2. Subtract the tax amount from the total price to find the original price:
Original price = Total price - Tax amount
Original price = $464.40 - $34.39
Original price = $430.01
Therefore, the original price of the FAX machine is $430.01, not $427.25.
For the textbook:
Tax rate = 9%
Total price = $158.60
1. Calculate the tax amount:
Tax amount = Total price * Tax rate / (100 + Tax rate)
Tax amount = $158.60 * 9 / (100 + 9)
Tax amount = $158.60 * 9 / 109
Tax amount = $158.60 * 0.0826
Tax amount = $13.08
2. Subtract the tax amount from the total price to find the original price:
Original price = Total price - Tax amount
Original price = $158.60 - $13.08
Original price = $145.52
Therefore, the original price of the textbook is $145.52, not $412.98.
To find the original price of an item when the final price including tax is known, you can use the following formula:
Original Price = Final Price / (1 + Tax Rate)
Let's apply this formula to the first scenario:
Original Price = 464.40 / (1 + 0.08)
Original Price = 464.40 / 1.08
Original Price ≈ 429.63
So, the original price of the fax machine is approximately $429.63, not $427.25.
Now, let's apply the same formula to the second scenario:
Original Price = 158.60 / (1 + 0.09)
Original Price = 158.60 / 1.09
Original Price ≈ 145.50
Therefore, the original price of the textbook is approximately $145.50, not $412.98.