An item is on sale at 40% off the regular price. It is taxed at a rate of 6%. If the final sale price including tax is $57.24, then what is the sale price of the item without tax? What was the regular price of the item?
The sale price of the item without tax was $________.
The regular price of the item is $____
If necessary, round to the nearest cent.
1.06x = 57.24
Solve for x for sale price.
(1-.4)x = sale price
Solve for x for full price.
To find the sale price of the item without tax, we can first subtract the tax from the final sale price.
First, let's calculate the tax amount:
Tax amount = (6/100) * $57.24
Tax amount = $3.4344
Now, let's subtract the tax amount from the final sale price:
Sale price without tax = $57.24 - $3.4344
Sale price without tax = $53.8056
To find the regular price of the item, we can use the relationship between the sale price and the regular price.
Sale price without discount = (100/60) * Sale price with discount
Regular price = (100/60) * $53.8056
Regular price = $89.6759
Rounded to the nearest cent, the sale price of the item without tax is $53.81, and the regular price of the item is $89.68.
To find the sale price of the item without tax, we need to work backwards from the final sale price including tax.
First, let's calculate the amount of tax added to the sale price. If the final sale price including tax is $57.24 and the tax rate is 6%, we can find the tax amount by multiplying the sale price by the tax rate:
Tax amount = $57.24 * 6% = $3.43 (rounded to two decimal places).
Next, we need to subtract the tax amount from the final sale price to find the sale price without tax:
Sale price without tax = Final sale price - Tax amount = $57.24 - $3.43 = $53.81.
So, the sale price of the item without tax is $53.81.
To find the regular price of the item, we need to account for the 40% discount. Since the sale price without tax represents 60% of the regular price (100% - 40%), we can set up the following equation:
Sale price without tax = 60% of regular price.
Now we can solve for the regular price:
Regular price = Sale price without tax / (60% or 0.60)
Regular price = $53.81 / 0.60 = $89.68 (rounded to two decimal places).
So, the regular price of the item is $89.68.