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How to solve problems related to marked price, selling price and discount.

This topic is part of the TCS FREE high school mathematics 'How-to Library'. It shows you how to solve problems related to marked price, selling price and discount.
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.


The situations described in this topic are from the point of view of the customer. Whenever you buy something at a discounted price, the following formula applies:

selling price = marked price - discount


'selling price' is what you actually pay for the thing,
'marked price' is the normal price of the thing without a discount, and
'discount' is either a dollar amount, or a percentage of the marked price.

Several problem types based on this formula are discussed in the examples below.

Example 1:

A quality pen that normally costs $20 is being sold for only $12. 
Calculate the discount in dollars, and also as a percentage of the marked price.

   Given: marked price = $20,  selling price = $12

selling price = marked price - discount

so discount = marked price - selling price

                       =   $20 - $12

                       =   $8

Expressing the discount as a percentage of the marked price:


     discount% =  -------------------------- × 100%

                                $marked price


                discount% =  -------- × 100%    =    40%


Example 2:

The usual price for an adult movie ticket at Big Screen Cinemas is $18.  
On Tuesdays they offer a 15% discount.

Calculate the cash value of the discount, and the cost of the tickets on Tuesdays.

   Given: marked price = $18,  

                          discount = 15% of marked price


                                  =  -------- × (marked price)



                                            =  -------- × $18



                                            =  $2.70


     So:        (selling price) = (marked price) - discount

                                             =  $18 - $2.70

                                             =  $15.30


On Tuesdays, the tickets cost $15.30

Example 3:

A music store has reduced all stock by 25%. A customer who purchased a CD from this store paid $24. What is the usual price of this CD, and what is the cash discount.

   Given: selling price = $24,  

                      discount = 25% of the marked price

   but:       (marked price) = (selling price) + discount


Expressing each of these quantities as percentages of the marked price, we have:

              marked price                         selling price                            discount

     (100% of the marked price) = (x% of the marked price) + (25% of the marked price)


So the selling price must be: (100-25 = 75)% of the marked price, ie:



      selling price    =     -------- × (marked price)




    marked price   =     -------- × (selling price)




                                =     -------- × 24



                                =  $32

The CD usually costs $32, and the cash discount is: (32-24) = $8.00


Maths Helper Plus can solve many kinds of discount problems. It will do calculations showing the working steps, as well as display a labelled diagram.  

Step 1 Download the free support file... We have created a Maths Helper Plus document containing the completed example from this topic. You can use this to practice the steps described below, and as a starting point for solving your own problems.

File name:  'Discount.mhp'   File size: 17kb
Click here to download the file.

If you choose 'Open this file from its current location', then Maths Helper Plus should open the document immediately. If not, try the other option: 'Save this file to disk', then run Maths Helper Plus and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.


Step 2  Display the parameters box

Press the F5 key to display the parameters box:


You enter the given information into these edit boxes as follows:


        edit box 'A' = marked price

        edit box 'B' = discount

You can enter the discount as a dollar value, or as a percentage of the marked price.

If the discount is in dollars, then set edit box 'X' to 0.

If the discount is a percentage of the marked price, set 'X' to 1.

        edit box 'C' = selling price


Set any two of A, B and C to the values you are given.

Set the unknown value to zero.

Out of the three edit boxes A, B and C, two will not be zero, and one will be zero.


NOTE: In the picture of the parameters box above, A=80, B=20, and C=0. This means we are solving the problem type where the marked price and discount are given, and we are calculating the selling price. Because 'X' is set to zero, the discount is $20, not 20%.


Click the 'Update' button to refresh the diagram and calculations.


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