# Percentage Discounts

Image Source: http://www.dobi.nu

The above TShirts were made by the very talented designer Rob Dobi.
You can buy Rob’s TShirts for around \$20 each online at the following link : http://www.merchline.com/fullbleed/

Let’s say that our favorite clothes shop is having a 15% off sale on Rob Dobi TShirts. In the shop we see a really nice shirt that has a price tag marking the shirt’s normal retail price as \$30.

In Mathematics, we call this normal retail price the “Marked Price” or “MP”.

Since the shirt is on sale at 15% off, we know that we are going to get a discount on the \$30 Marked Price, and pay less than \$30 for the shirt.

The amount we are taking off the normal Price is called the “Discount”.

The discount is how much money we are going to save if we buy the shirt during the sale, rather than buy it for the normal recommended retail price.

We can calculate the discount as follows:

Discount = 15% of Marked Price

(remember “%” means / 100 and “of” means multiply)

= (Discount % / 100) x Marked Price
= 15 / 100 x \$30
= 15 divided by 100 x \$30
= \$4.50

So the dollar saving we will make during the Sale is \$4.50

For calculating the Discount \$, the Algebra formula is as follows:

Discount = (Discount% / 100) x MP (where MP = Marked Price)

The Price we actually pay for the shirt is called the “Selling Price”, “Sale Price”, or “SP”.

For calculating the Selling Price, the Algebra formula is as follows:

Selling Price = Marked Price – Discount

For our shirt the Selling Price is:

SP = MP – Discount
= \$30 – \$4.50
= \$25.50

So we will pay \$25.50 for our shirt, if we buy it on sale.

In this lesson we look at how to work out Percentage Discounts.

Percentage Discounts – Key Words

There are a number of special words that are used when we talk about selling items for profit.

These will become more familiar as we work through this lesson.

Here are the set of Key Words we need to know for dealing with Discounts.

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Algebra Formulas for Discount Questions

To calculate Discount and Selling Price, we use the following mathematical formulas.

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Selling Price (Multiplying Factor Method)

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Another way of determining the Selling Price is to use a method involving a “Multiplying Factor”.

The multiplying factor “M.F.” is a decimal value that we can multiply by the Marked Price to get the Selling Price.

In this method we use the following two formulas :

M.F. = (100% – Discount %) / 100

and then we calculate the SP using our M.F. answer like this:

SP = M.F. x MP

For our \$30 shirt with a 15% Discount, the calculation is:

M.F. = (100% – Discount%) / 100

-> Substitute in our Discount% of 15

M.F. = (100 – 15) / 100
M.F. = 0.85

SP = M.F. x MP

-> Substitute in M.F.=0.85, and MP=\$30

SP = 0.85 x \$30
SP = \$25.50

Percentage Discount or Percentage Saving

So far we have been looking at working out the Discount dollars for an item that is on sale, when we know what the Discount% value is.

Now let’s look at working backwards and finding the Discount% .

If we buy something on sale, then we can calculate the percentage we saved by doing the following steps.

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The following example shows how to use these steps to do a Percentage Discount question.

Discount Percentage Example

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Let’s say we go to a clearance store and they have a pair of Nike sports shoes we like, with a Marked Price on them of \$110.

We really want to buy these shoes, but only we only have \$90 to spend.

We tell the sales person we will offer them \$80 for the shoes.

They talk to their manager and then tell us we can have the shoes for \$90.

What is the percentage discount they have given us?

We need to follow the steps:

Work out Discount = Regular Marked Price – Sale Price
then
Divide by the Marked Price
then
Multiply by 100%

Discount = \$110-\$90 = \$20

Next Divide by the MP which gives us: \$20 / \$110 = 0.181818

Now Multiply by 100% which give us: 0.181818 x 100% = 18.1818%

So we have managed to get an 18% Discount on the Shoes.

We can also represent this process by the following Algebra Formulas:

Dollar Discount = MP – SP

and

% Discount = (Dollar Discount / MP) x 100%

or combine everything into a single formula like this.

% Discount = ((MP – SP) / MP) x 100%

If you are using a Calculator to work out the answer, then putting in the brackets shown above is extremely important.

Let’s use the single formula to work on the \$110 shoes being sold to us for \$90.

For this example, MP = \$110 and SP = \$90

% Discount = ((MP – SP) / MP) x 100%

= (( 110 – 90) / 110) x 100

= (20 / 110) x100

On calculator do 20 divided by 110
and then multiply by 100

= 18.1818

= 18%

Discounts Summary

The following is a summary of the formulas we need to know for doing questions involving Percentage Discount.

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Discounts Videos

The following video is by “YourTeacher.com”, and shows how to calculate a Discount and then work out the Selling Price.

This next video is by a mathematics teacher, and also shows how to how to calculate a Discount and then work out the Sale Price.

This final video covers everything we have done in this lesson.

In particular, six and a half minutes into the video, we see how to calculate the dollar discount as a percentage value.

Discount Calculator

We can use this calculator to get discounts. But this calculator is extra nice, because we can also enter the “Reduced” discounted price, and will it will calculate the original price.

So the calculator works in both directions.

Note that we always have to enter the Percent Value, but we only have to enter one of the three items on the top input line.

http://discount.miniwebapps.net/

Percentage Discount Game

This game teaches how to calculate percentages, as well as rounding off Answers. It is a UK game, and so money is in pounds and pence.

Click here to play Percentages Discount Game

Percent Discount – Discounts at Troy’s Toys

This game is quite challenging, and for some people they might need a calculator to divide the % value by 100, and then multiply by the dollar amount.

http://www.mathplayground.com/percent_shopping.html

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