Jackson purchases a pack of games cards that was on sale for 22% off. The sales tax in his county is 6%. Let y represent the original price of the cards. Write and expression that can be used to determine the final cost of the cards.

Short answer: The final price = 0.8268 * the original Price

This may be a little long winded but it is easier to see than if I just give the answer.

Original cost of the deck of cards = y

The sale price can be firgured out in two ways.

1. y - (22/100) * y

y - 0.22y

y * (1 - 0.22)

0.78y is the final sale price

2. You could just do the last step right away.

y * (1 - 0.22) = 0.78y is the sale price.

Now you add the sales tax. You don't do that until a sale of any kind has been made.

So you need to add on 6% to the number you already have. Again you can do it in two ways.

You can take 6% of 0.78y and add it on which is the way I'll do it.

0.78y + (6/100) * (0.78y)

0.78y + 0.06*0.78y

0.78y + 0.0468y

0.8268 y is the final amount that has to be paid.

Jackson gets 22% of the price taken out of the total and 6% of the price added to the total. I would write an equation like this, with P representing the final price of the cards:

P = y - 0.22y + 0.06y

Simplified, it looks like this:

P = 0.84y