SOLUTION: On a sale, Jose got a 10% discount on the original price, but a 10% tax was added to the selling price. Did Jose pay an amount equal to the original price?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: On a sale, Jose got a 10% discount on the original price, but a 10% tax was added to the selling price. Did Jose pay an amount equal to the original price?      Log On


   

Question 557115: On a sale, Jose got a 10% discount on the original price, but a 10% tax was added to the selling price. Did Jose pay an amount equal to the original price?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
no, because the 10% discount was applied to the original price while the 10% tax was applied to the sale price.
since the sale price was less than the original price, the tax on the sale price was less than the discount.
algebraically this is seen as follows:
let x = the original price.
discount of 10% on the original price is applied as follows:
sale price = x - .10*x which is equal to .9*x
you have a sale price of .9*x.
now you want to apply a 10% tax on the sale price.
that is applied as follows:
sale price + tax = .9*x + .1*.9*x
simplify this equation to get:
sale price + tax = .9*x + .09*x
combine like terms to get:
sale price + tax = .908*x
the original price is x.
the sale price is .9*x
the sale price + tax is .908*x
the 10% tax on the sale price is less than the discount because the 10% tax is taken off the sale price which is a smaller figure than the original price.
let's look at it from numbers.
assume the original price is 100 dollars.
the sale price would be 100 dollars minus 10% of 100 dollars which equals 90 dollars.
the sale price is equal to 90 dollars.
the tax on the sale price is equal to 10% of 90 dollars which is equal to 9 dollars.
you have a discount of 10 dollars and a tax of 9 dollars.
the original price was 100 dollars
jose paid 99 dollars.