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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.)Â To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.

### Theory:

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

Where:Â Â Â Â Â Â Â

'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.Â
Calculate the discount in dollars, and also as a percentage of the marked price.

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

selling price = marked price - discount

so discount = marked price - selling price

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  =Â Â  \$20 - \$12

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  =Â Â  \$8

Expressing the discount as a percentage of the marked price:

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  \$discount

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  \$marked price

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  \$8

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  \$20

Example 2:

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

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

Â Â  Given: marked price = \$18,Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  discount = 15% of marked price

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  15

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  100

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  15

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  =Â  -------- × \$18

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  100

Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  =Â  \$2.70

Â

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  =Â  \$18 - \$2.70

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  =Â  \$15.30

Â

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.

Â Â  Given: selling price = \$24,Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  discount = 25% of the marked price

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

Â

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

Â Â Â Â Â Â Â Â Â Â Â Â Â  marked priceÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  selling priceÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  discount

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

Â

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

Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  75

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  100

So:

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  100

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  75

Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  100

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  =Â Â Â Â  -------- × 24

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  75

Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  =Â  \$32

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

### Method:

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. Â

Â

#### Step 2Â  Display the parameters box

Press the F5 key to display the parameters box:

Â

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

Â

Â Â Â Â Â Â Â  edit box 'A' = marked price

Â Â Â Â Â Â Â  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.

Â Â Â Â Â Â Â  edit box 'C' = selling price

Â

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.

Â

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%.

Â

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

Â