Question

Jerome bought a sweater that was on sale for 20 percent off. Jerome paid $25.10 for the sweater, including sales tax of 8.25 percent. Write an equation that can be used to find the original price of the sweater.

Answer 1

Let the original price of the sweater be = X
Then the amount Jerome pays for the sweater after 20% discount = X - (20X/100)
                                                                                                           = X - 0.2X
                                                                                                            = 0.8X
Now on this price the 8.25% tax needs to be added to get to the amount actually paid by Jerome.
So,
0.8X + [(8.25/100) * (0.8X) = 25.1
This is the equation from which the actual price of the sweater bought by Jerome can be determined.
So
0.8X + [(.0825) * ( 0.8X) = 25.1
0.8X + 0.066X = 25.1
0.866X = 25.1
X = 25.1/0.866
   = 28.98
So the actual price of the sweater is $28.98.