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.
To find the sale price of the item without tax, we need to first calculate the price before tax and then subtract the tax amount.
1. Let's assume the regular price of the item is 'x' dollars.
2. The sale price of the item at a 40% discount is calculated as (100% - 40%) * x = 60% * x = 0.6x dollars.
3. Now, we need to add the tax to the sale price. The tax rate is 6%, which can be represented as 0.06 (decimal form).
4. The final sale price including tax is given as $57.24, so we can set up the following equation:
Sale price + (tax rate * Sale price) = Final sale price
0.6x + (0.06 * 0.6x) = 57.24
Simplifying the equation: 0.6x + 0.036x = 57.24
Combining like terms: 0.636x = 57.24
Dividing both sides by 0.636: x = 57.24 / 0.636
Let's calculate the sale price without tax and the regular price based on this equation:
1. Sale price without tax = 0.6x dollars
Substitute the value of 'x' into the equation: Sale price without tax = 0.6 * (57.24 / 0.636)
2. Regular price = Sale price without tax + Tax amount
Regular price = (0.6 * (57.24 / 0.636)) + (0.06 * (0.6 * (57.24 / 0.636)))
Calculating these values will give us the answers:
Sale price without tax = (0.6 * (57.24 / 0.636))
Regular price = (0.6 * (57.24 / 0.636)) + (0.06 * (0.6 * (57.24 / 0.636)))
Now, let's perform the calculations to find the answers.