Applied Percents – Discounts

Discount Mathematics
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In our previous lesson we looked at how Retailers place “Mark Ups” on items so that they can make a Profit on the sale.

It is important that you have viewed this lesson before doing the contents of our Discount and Loss Lesson.

The Mark Up and Profit Lesson can be viewed by clicking the link below:


Definitions for Items in Formulas


Cost Price

The Cost Price is how much it costs a retailer to buy items they are going to sell from suppliers or from overseas.


Mark Up

The Mark Up is extra money that the retailer adds on before putting a final price on the item.


Marked Price

This is the final price of the item. The Marked Price is then written onto the tag or sticker that is put onto the item in the shop.

This is the price the customer has to pay for the item and is also often called the full “Recommended Retail Price” or “RRP”.

If the item is NOT on discounted sale, then the customer has to pay the full RRP that is on the item’s tag or sticker.



If the shop is having a Sale, you do not have to pay the full Marked Price on the item. This is because the retailer gives you some money off the full normal price to create a lower than normal “Sale Price”.


Sale Price

The Sale price is the price the customer ends up paying for the item.

If the item is on sale for a discounted price, the Sale Price (sometimes called the “Selling Price”), will always be lower than the full normal Marked Price.

But if the item is not on sale, the customer will have to pay the full normal Marked Price.



Retailers sell items for more than it cost to get them, (even when the items are on Discount Sale). This allows the Retailer to make some money.

The money that the retailer makes from selling the item is called the “Profit”.



Sometimes a retailer will get into money problems, or have more items than they can fit in their shop or warehouse.

When this happens they have to sell goods at desperately low prices to get money to pay for shop rent, wages, electricity, transport, etc.

If they do not take this desperate step, they will get into huge debt and go out of business.

If they have to sell an item for less money than it originally cost them, then they will lose money on that item.

Losing money on a sale because the Sale Price is really really low, is called “Making a Loss”.


GST – Goods and Services Tax

Most goods in Australia are subject to a 10% “GST” Tax, except for some basic grocery and food items.

This means that 10% tax is included in the price the customer pays.

When a Retailer gets the original item at Cost Price, then does the Mark Up, then might give a sale Discount, there is a resulting final price the customer is going to pay.

In most cases, 10% of the money which the Retailer gets from the Sale has to be forwarded by the Retailer to the Goverment as GST.

Retailers need to be aware in their Financial Planning that 10% of all their profits are taken away by the Government as GST Tax.

This means that Retailers need to average more than 10% Profit on their Sales. Otherwise they will not make any money and will go out of business.


Discount and Selling Price

Tommy and Tamara TV Shop Pic
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Tommy and Tamara’s TV Shop are having a “10% off” sale.

This means that customers can get any TV on sale for 10% cheaper than the normal Marked Price that is on the price label on the TV.

We say that customers are getting a “10% Discount” or that they are making a “Saving of 10%”.

The following digram shows the mathematical formula we use for calculating the sale price of a TV which is discounted by 10% during the sale.

Discount Mathematics One
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Discount Dollars

We can calculate the Discount amount (which is the amount saved) using the formula:

Discount Dollars = Marked Price – Selling Price

This is shown in the following diagram:

Discount Calculatrion Two
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Working Backwards to Find Marked Price

If we know the Sale Price, and the Percentage Discount, we can work backwards to find the original “Marked Price” by using the following Formula:

Marked Price Calculation Three
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Note that we have written the formula in a form which shows how it must be typed into a Calculator to get the correct value for Marked Price.


Price the Customer Pays

Paying with Cash
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The discounted price which the customer pays is called the “Selling Price”.

Discount Mathematics Five
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Discount Formulas Summary

Here are the main formulas we use for working with Discounts.

Discount Mathematics Ten
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These need to be copied down into the maths notes for Discounts in your workbook.


How to Select the Correct Formula

Choosing Clip Art
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To choose the best formula to use for a financial mathematics word problem, we do these steps:

1) Identify the unknown – eg. what is it we need to find the missing value of (Marked Price, Selling Price, Discount $, %Discount, etc).

Make sure that the unknown item is on the left hand side of our formula.

2) Identify what is given to us in the problem out of Marked Price, Selling Price, Discount $, %Discount, etc.

Make sure the given items are on the right hand side of the formula.

Discount Mathematics Twelve
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Videos About Doing Discounts


Here is a quite detailed Video about Discounts and Sale Price.


Discounts Online Calculator

Percent Discount

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.


Related Items

In our previous lesson we covered Cost Price, Mark Up, and Profit. Click the link below to check out this lesson.


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