At a certain store, employees may buy clothing at a 20% discount from the original price, but must pay a 6% sales tax. If the final cost of a sweater purchased by an employee is $55.12 what is the original price of the sweater, before the discount and tax? Explain please

Po - 0.20Po + 0.06Po = $55.12, 0.86Po = 55.12, Po = $64.09 = Original price.

To find the original price of the sweater before the discount and tax, we can use the following steps:

Step 1: Calculate the price after the discount.
Since employees get a 20% discount, they pay 80% of the original price. We need to find the price after this discount. Let's call it P1.
P1 = 0.8 * P (where P is the original price)

Step 2: Calculate the price after adding the sales tax.
The final cost of the sweater is $55.12, which includes a 6% sales tax. To find the price before the tax, we need to back-calculate by dividing the final cost by (1 + tax rate in decimal form). Let's call it P2.
P2 = $55.12 / (1 + 0.06)

Step 3: Equate P1 and P2 to find the original price.
P1 = P2
0.8 * P = $55.12 / (1 + 0.06)
Now, we can solve this equation to find the value of P, which will be the original price of the sweater.

By following these steps, you will find the original price before the discount and tax.