Pre Algebra (Period 2 & 4)

Discount & Markup 10-6

This is when we rush out to go shopping! :)


DISCOUNT = The amount OFF when something is on sale


The calculation is similar to Tax and Tip in that you still

MOVE IT, MOVE IT, MULTIPLY

The difference is that instead of adding to what you had,
this time you will SUBTRACT



EXAMPLE:
A jacket that was $100 is now 35% off.


MOVE IT, MOVE IT, MULTIPLY
Discount = (.35)($100) = $35


SUBTRACT THIS "DISCOUNT" FROM THE ORIGINAL PRICE

Sales price = $100 - $35 = $65



YOU CAN DO THIS IN ONE STEP:

In the example above, you are NOT PAYING the 35% DISCOUNT

So what % are you paying?

65% (100% - 35% discount %)

Finding the sales price in one step:
($100)(.65) = $65



Again, this is what you do to find the SALES PRICE in ONE STEP:

100% - DISCOUNT% = % you will pay

Then move it, move it, multiply

And you won't have to subtract!

You'll already have the SALES PRICE!


What if you know what the price is on sale, you know the original price, and you're trying to figure out if this is a really good % off?


Can you figure our what % off this is????

Yes you can because the...

The DISCOUNT% = a % of DECREASE!



When would a store not state the % off?

This usually happens when items are on sale in the supermarket.

They don't state the % off.
They just tell you what the sales price is.

Why do you think they do that?
Usually when the Discount% is small.
It also happens whenever the % is strange amount (not a multiple of 5).


EXAMPLE at a supermarket - small and strange:
Fruit snacks are 50 cents off a box of 10
Original Price: $3.99
Sales Price: $3.49
Sales Discount % = discount/original = $.50/$3.99 = .125
or about 13% off
 
EXAMPLE at a store where an item is on clearance - clearance item %s off vary depending on how long an item has been on clearance:

You look at the price tag on a jacket and see that the original price = $200
and sales price = $50.
You know this is a great price, but still you're wondering what is the DISCOUNT %?
(% of decrease?)

Decrease or discount = original price - sales price

$200 - $50 = $150 discount (amount off)


What is this as a % off? Calculate the % of decrease:

$150 decrease/$200 original = 3/4 = 75% Discount &


WOW! THAT'S A GREAT SALE!!!


EXAMPLE where % is a strange amount so the store just states it as a certain number of dollars off (instead of as a %):

You look in the Best Buy weekly flyer. The sales price on a computer is $700.

The original price is $770.

What is the amount off (the discount)?
$770 - 700 = $70 discount


What is this as a sale discount %?

Discount/Original = $70/$770 = .090909... or about 9%


NOT REALLY A GREAT % OFF SALE!
(but you ARE still saving $70!)



ANOTHER REASON WHY SUPERMARKETS GENERALLY NOT USE % OFF:


The %s are usually small AND they are all different.


One item might be 13% off and the item next to it might be 9% off.

It would drive shoppers crazy to figure out all those different percentages that only end up being say $.50 off!


Whereas, when Macy's has a sale, clothes tend to be all 20% off (for example)


Original prices are much higher and the % off used tends to be the same for each item.


What about sales that are stated as fractions off?

1/3 off sale, 1/2 off sale

You won't have to move it, move it!

You'll just multiply and subtract!



FRACTION EXAMPLE:

A $900 LCD TV is 1/3 off

Discount = (1/3)(900) = $300 off

Sales price = $900 - 300 = $600



YOU CAN FIND THE SALES PRICE IN ONE STEP:


You're NOT PAYING 1/3 of the price.
What fraction are you PAYING?

1 (whole original price) - fraction off = fraction of the original you are paying


1 - 1/3 = 2/3


In the example above with the LCD TV:
(2/3)($900) = $600 on sale



SALES THAT ARE STATED AS RATIOS:


Sales are stated like this:

Buy 2, get 1 free

Buy 1, get the 2nd one for a penny

Get 3 for $10 (but when you buy less than that, the price/item is $3.99)



Papa Johns has a sign that states: Buy 1 pizza at regular price, get the 2nd for a penny.

What % off is this?

Well first of all, in the real world, the first pizza price will vary based on what you get on it.


Let's just assume that your first pizza is $15.

The first pizza is 100% of the original cost...it is NOT on sale.


But then you add a 2nd pizza of the same price and pay a penny.


You have paid $15.01 for 2 pizzas.
You would have paid $30.00 for the 2 pizzas without this "deal"


DISCOUNT % = discount (decrease in price) / original price


DISCOUNT % = $30 - $15.01 / $30 = $14.99/$30.00 = about 50%


SO THIS IS A HALF PRICE SALE FOR THE 2 PIZZAS!


WHY NOT JUST MAKE EACH PIZZA HALF PRICE????

Because you might just buy 1 pizza for $7.50 and not buy the 2nd pizza!

When does this make sense for the company?


When they are looking for incremental (more) sales and the cost of the 2nd item is not going to be sold at a loss. (pizzas don't cost $15 to make!)
 
I ALWAYS BUY A LOT MORE CHEWY CHIPS AHOYS WHEN PAVILLIONS HAS THEM AS BUY 1 GET 1 FREE.
That's a half price sale! Make sure you buy an EVEN number of them or the last one is at full price!