Passy's World of Mathematics

Cost Price Mark Up and Profit

Posted on February 10, 2013 by Passy

Image Source: http://www.floridatoday.com

In the next couple of lessons we are looking at the Mathematics of Retail Businesses.

This will involve using Buying Selling and Discounting Formulas.

This includes the retailer getting goods to sell, and applying a price increase so that they can make money on each sale.

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

Discounts that occur during sales are also covered.

Finally, the sad situation of selling goods at a “Loss” is also covered.

To work out the mathematical answers required for Retailers and Buyers of products, we use various Maths Formulas.

The tricky bit is figuring out which formula to use for a given retail situation. Several practical examples are given to help people get good at this.

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.

Discount

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.

Profit

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”.

Loss

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.

Cost Price, Mark Up, and Marked Price

Image Source: http://www.star1045.com.au

Tommy and Tamara’s TV Shop gets a Samsung TV from Asia at a cost of $1000.

They need to sell the TV for more than $1000 so they can cover their running costs such as shop rental, electricity, accounting costs, taxes, and so on.

To do this they put a “Mark Up” of 80% on the TV to create the “Marked Price” that will be on the sale sticker on the TV in their shop.

The “Cost Price” of the TV was $1000

80% of $1000 = $800

This means the “Mark Up” added onto the original Cost Price will be $800.

This makes the “Marked Price” of the TV become $1800.

The Mathematics of this is summarised in the following diagram:

Marked Price – Working Backwards

Image Source: http://cdn.sheknows.com

Tommy and Tamara have a Panasonic TV for sale in their shop with a Marked Price of $1600.

If we know that the Mark Up % on this TV is 90%, what was the original “Cost Price” of the TV ?

This question if a “working backwards” Marked Price question.

From working with Algebra Equations, we know that working backwards involves applying opposite operations.

Our previous Marked Price Formula had MULTIPLICATION in it, so we need to change this to use DIVIDED BY.

Here is how we work out the above Panasonic TV question:

Marked Price – Video

Here is a Quick Video about Markup

Marked Price – Summary

The following diagram shows a summary of the formulas we use for questions which involve Marking Up products.

Selling Price

Image Source: http://www.goldrushstores.com

The Price the customer pays of an item is called the item’s Selling Price.

The Selling Price is how much it costs the customer to buy the item.

If there is no Discount on the item, then the customer has to pay the full Marked Price that is on the item.

If the customer gets a Discount, (eg. money taken off the full price because it is on sale at a certain percentage reduction), then the Selling Price is the Marked Price take away the Discount.

This is summarised in the following diagram.

Mark Up Formulas Summary

Here are the main formulas we use for working with Mark Ups.

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

How to Select the Correct Formula

Image Source: http://info.sybiz.com

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, Cost Price, Mark Up $, %Mark Up, 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, Cost Price, Mark Up $, %Mark Up, etc.

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

Dollar Profit

The “Profit” is how much money the Retailer makes on selling the item.

This dollar profit is the difference between how much the Retailer originally gets the item for, and how much the Retailer is able to sell the item for.

Dollar Profit = Selling Price – Cost Price

Remember that if there is no Discount, then the Selling Price is the full Marked Price on the Item.

This is summarised in the following diagram.

Percentage Profit

Profit is often expressed as a “Percentage Profit”.

There are two ways businesses used to express Percentage Profit as follows:

1) Percentage Profit based on the Cost Price

and

2) Percentage Profit based on the Selling Price

This can be very confusing for people new to Financial Mathematics. The trick is to read the given question or situation very carefully.

If the question just asks for “Percentage Profit” (and does not specify based on Selling or Cost), then calcualte the Percentage Profit based on the Cost Price.

Shown below is how we calculate the Percentage Profit based on the Cost Price for a TV which cost $1000 and was sold for $1620.

Shown below is how we calculate the Percentage Profit based on the Selling Price for a TV which cost $1000 and was sold for $1620.

Percentage Profit and Gross Profit

The Percentage Profit based on the Selling Price is often referred to as the “Gross Profit”.

It is when we compare the Profit to how much we are making on an item compared to how much money that sale brings into our business.

The “Gross Profit” based on Selling Price is always lower than percentage claculated based on the Cost Price.

This is explained in the following video.

Profit Formulas Summary

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

These need to be copied down into the maths notes for Profits in your workbook.

Africa Trip to Ruben Centre

Posted on February 3, 2013 by Passy

We have not been doing any work on Passy’s World of Mathematics over the last month or so. This is because we have been working on other projects while vacationing in Africa.

We are now back home in Australia, and we will definitely be adding new material to the website over the next few weeks.

Our main reason for going to Africa was to promote Passy’s World in South Africa, visit the Ruben Centre in Nairobi Kenya, and also do some tourist sight seeing.

It was certainly a very busy trip, and one which has left some very deep and lasting impressions.

The most moving experiences happened while seeing local people living their daily lives.

The struggle for basic survival occurs daily for most of the people in African countries. It is harsh and unforgiving. As many African people told me: “Survival is by the Grace of God”.

The Ruben Centre

A small group of four teachers and I ventured deep into the slums of Nairobi and visited the Ruben Centre.

At the Ruben Centre, we were met by Brother Frank, who has been doing missionary work throughout Africa for the last 30 years.

The Centre is managed by the Christian Brothers, but was initially started by the Sisters of Mercy from Ireland in 1986.

Ninety people are employed at the Centre, which is enclosed within a walled secure compound, and includes a Medical Centre and a School.

The medical centre sits within the same secure compound as the school, and last year treated 57 000 cases of illness.

350 of these were HIV positive. In the photo photo below you can see some women with new born babies.

Most of the girls we saw with these babies appeared to be teenagers. We shuddered at the thought of their stories, let alone their future.

Brother Frank was extremely proud of the programs that are running here. For example: Micro credit, teaching women self defence to protect them against sexual assault / family violence, protection against abuse of child labor.

As well as the Medical Centre, there is also a local school which educates children from the slum district.

The Ruben school is growing at a rapid rate. 1800 students currently attend the school.

Years 1 to 8 students attend the centre, and they then do the final four years of Secondary school at other schools.

A frightening mathematical statistic is that more than 50 percent of all university graduates will be unemployed if they stay in Nairobi.

In Year 1 there are 230 students and 2 TEACHERS ONLY !

In Year 2 there are 140 students and 2 TEACHERS ONLY !

All students are taught in the first language of English, and not in their native language of Swahili.

Students are fed on site, (The UN contributes money towards this).

At morning break, students drink a type of rice milk. No complaints and they all look wonderfully healthy. They also receive another hot meal at Lunchtime. No childhood obesity problems here! Students are healthy and slim, and in several classes they comfortably sit two aside in large plastic outdoor furniture chairs.

1800 students racing around at recess but no teachers on duty. Not required!

During our time at the school, we joined the students in many activities, including Reading in the Library, Learning in Classes, Outdoor Sports including Gymnastics and Music, and looking after the extensive horticultural facility with its plants and livestock.

It was certainly a moving and unforgettable experience.

More information about the Ruben Centre can be found by clicking the link to their website below:

http://www.rubencentre.org/

We nearly forgot to put something Mathematical into this review!

The photo below shows a partially completed human triangular pyramid. Rest assured that the students did know what a triangle shape looks like, it was just that one boy with a sore foot was not able to take up his position to finish the Pyramid!

Sight-Seeing Pictures

There was plenty of time-off during our three and a half weeks in Africa to do some sight seeing and touring, mainly around the country of South Africa.

We went off in search of local wild life.

We had some down time chilling at the beach.

We checked out places of geographical interest.

And ended up having the locals eating out of our hands!

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Passy

Posted in Math in the Real World | Tagged African School, Passy Africa Trip, Passy in Africa, Passy's World in Africa, Ruben Centre, Ruben Centre Nairobi Kenya, Ruben Centre School | Leave a comment

Mathematical Christmas Decorations

Posted on November 26, 2012 by Passy

Here’s a great idea for decorating your Maths Classroom for the festive season – Polyhedra and Geometrical Solids!

A friend of mine had her class make various three dimensional solids out of colored paper, and then hung these up along the wall of her classroom.

As well as making the actual shapes, students also wrote some witty mathematical christmas greetings onto their solids.

Additional witty greetings not shown here are:

Santa finds all the houses, he uses the Distributive Law to make sure!

Giving is Greater Than Receiving

Joy, Giving, and Celebration – The Christmas Triangle

Don’t be Mean and say anything Negative

Y is it called Xmas ?

Rise early and Run to the Tree!

Santa told me that Al G. Bra has been a very good boy!

Making the Shapes

Plenty of free Net Layouts can be found on the Internet for building the shapes, and the shapes shown in these photos were made from materials available at the following websites:

http://www.worksheetworks.com/math/geometry/polyhedra.html

http://www.korthalsaltes.com/

Finally thanks to Ms Fatima Nazar and her students for sharing this great idea on Passy’s World.

Note that students appearing in this post are under the age of 18, and have had their parents sign standard “Model Release” forms, granting permission for the images of the students to appear in this lesson.

Help Passy’s World Grow

Each day Passy’s World provides hundreds of people with mathematics lessons free of charge.

Help us to maintain this free service and keep it growing.

Donate any amount from $2 upwards through PayPal by clicking the PayPal image below. Thank you!

Subscribe to Passy’s World

If you enjoyed this lesson, why not get a free subscription to our website.
You can then receive notifications of new pages directly to your email address.

Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.

To find out exactly how free subscription works, click the following link:

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If you would like to submit an idea for an article, or be a guest writer on our website, then please email us at the hotmail address shown in the right hand side bar of this page.

Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.

Enjoy,
Passy

Posted in Geometry, Math in the Real World | Tagged chistmas maths activities, christmas math activities, christmas mathematics, christmas mathematics activities, decorating math classroom, geometry nets, geometry solids, how to make a polyhedron, make geometric solids, making 3d shpes, making polyhedra, math models, math xmas decorations, mathematical christmas decorations, nets for solids, polyhedra models, polyhedra nets | Leave a comment

Mathematics of the Melbourne Cup

Posted on October 31, 2012 by Passy

Image Source: http://www.theepochtimes.com

Bart Cummings is the “Cups King” – the horse trainer who has won more Melbourne Cup races than anyone. Long Live the King!

In this lesson we look at some of the mathematics associated with Austrlia’s premier horse racing event: “The Melbourne Cup” which is held annually on the first Tuesday in November.

It is a long race totalling 3200 meters, (Or around 2 miles), and lasts for around three and a half minutes.

There is very large prize money on offer, and it attracts an international field of champion race horses.

With the actual horse race only a few days away, this lesson is a bit of a rushed job. We hope to add more to it at a later stage, and have a fuller list of items here for the 2013 Melbourne Cup.

Betting Odds

Image Source: http://www.theage.com.au

If you placed a bet of $1 on a horse, what dividend would be payed to you if the horse won?

Odds can be a bit misleading, so it is always worth also looking at the actual probability of winning.

For every winner, there are plenty of people who invest their money for zero return.

The information at the following link explains the difference between odds and probability.

http://mathforum.org/library/drmath/view/56701.html

The Odds always give the track “bookie” or the betting company the edge.

Melbourne Cup Statistics

Image Source: Picture on Google but could not be found on Getty Images website

The following website has some great Melbourne Cup Facts and Figures:

http://www.races.com.au/melbourne-cup/melbourne-cup-history/facts-and-statistics/

Here are a few interesting facts and figures.

Melbourne Cup Barrier Statistics

•Barrier 18 is the only gate never to produce a winner since barriers came in in 1924
•The most successful barriers have been 9 – 12 with four victories in the past 11 years

Melbourne Cup Saddlecloth Statistics

Numbers 4 and 12 are the most successful boasting 11 wins
•No 4 and No 12 with 11 wins
•No 1 with 9 wins
•No 8 with 8 wins
•No 11 with 7 wins

•TAB numbers 4 and 6 have won four of the last fifteen Cups.
•TAB numbers to win only one Cup are 26, 28 and 39.
•TAB numbers to win only two Cups are 7, 16, 18, 21, 23 and 25

Melbourne Cup Winner Stats – Age

•Four and five year old horses have the best record with 43 winners each
•In the past 11 years however six-year-olds have won five times most recently Dunaden (2011)
•Only two eight-year-olds have won the Melbourne Cup

Melbourne Cup Winner Stats – Horse Type

•In the past 12 years five Melbourne Cup winners were mares

•Stallions (Entires) hold the record with 64 wins

•Entire 64
•Gelding 50
•Colts 21
•Mares 13
•Fillies 3

Melbourne Cup Weight Facts

•In the past decade the average Melbourne Cup weight carried to victory is 54kg
•Heaviest weight carried to victory was Carbine, sire of Phar Lap, with 10 stone 5 pounds (66.0kg) in 1890
•Phar Lap actually carried the highest weight with 10stone 10lg (68kg) but lost
•Lowest Weight carried to victory was Banker with just 33.5kg in 1863

Melbourne Cup Winning Colours

•17 cup winning jockeys have worn black as their main colour, the last being George Podmore on Evening Peal in 1956.
•Navy blue and royal blue with 14 wins

Melbourne Cup Betting Favourites

•Melbourne Cup betting favourites have won 32 times in 151 years, eg. only about 20% of the time.

Information Source: http://www.races.com.au/melbourne-cup/melbourne-cup-history/facts-and-statistics/

Total Prize Money

Information Source: http://en.wikipedia.org/wiki/Melbourne_Cup

The above table shows the total prize money for the Melbourne Cup Race over the last few years.

The first 10 horses past the post receive prize money.

In the 2011 race, with a total prize pool of $6,175,000 – the winner was paid $3.3 million, and tenth place $115,000.

Prize money is distributed to the connections of each horse in the ratio of 85 percent to the owner, 10 percent to the trainer and 5 percent to the jockey.

So for the first place horse in 2011, how much did the trainer and jockey each receive ?

For the tenth place of $115,000 how much did the trainer and jockey each receive ?

A further activity would be to draw a side by side comparison bar chart for these dollar figures.

Another mathematical exercise we can do on this data, is determine how much the total prize money has increased each year, as a percentage of the previous year.

Here are the answers we obtained using a Microsoft Excel Spreadsheet.

Crowd Attendances at Melbourne Cup Carnival

Image Source: http://static.stuff.co.nz

From what we hear and see in the Media here in Australia, crowds at the racing are portrayed as being huge and ever increasing.

For example, here is a media report from the internet relating to the 2011 Melbourne Cup.

“The four days of the Melbourne Cup Carnival attracted the four biggest attendances of any racing event in Australia:

AAMI Victoria Derby Day: 92,336
Emirates Melbourne Cup Day: 105,979
Crown Oaks Day: 71,659
Emirates Stakes Day: 85,112

2011 Melbourne Cup Carnival Total: 355,086 (1,908 more than 2010) ”

Information Source: http://formguide.cyberhorse.com.au

A full set of historical crowd attendances at all Cup Carnival Events is available at the following web page:

http://melbournecup.com/racing/race-results-statistics/track-attendances/

This data provides opportunities for a number of Graphing and Statistics activities.

For example, here at Passy World we examined the last few years of cup races, and obtained the following results.

(Click the above Image to view full size)

As can be seen quite clearly: Melbourne Cup attendance is fairly steady, Derby Day and Oaks Day have both been declining, but Stakes Day (possibly due to recent Emirates Airlines sponsorship and profile raising) has been increasing.

Oaks Day is traditionally a ladies day of fashions at the races and occurs on the Thursday following Melbourne Cup Day in November each year. An interesting activity would be to use Calendars and Melbourne Weather records to see if there is a correlation between Oaks Day attendance figures and the Weather.

Image Source: http://resources0.news.com.au

Eg. We could Graph Oaks Day Attendance against Daily Temperature, and determine a “Line of Best Fit and the “Correlation Coefficient”. There is a great free online graphing application that does this sort of analysis at the following link:

http://nlvm.usu.edu/en/nav/frames_asid_144_g_4_t_5.html?open=activities

We may also be able to graph Attendance against Wind Speed and check for Correlation.

As both Oaks Day and Derby Day Attendances have been declining the last few years, we could also do a Correlation between these two events and see if there is any mathematical relationship.

Additional Ideas for Cup Day Mathematics

Image Source: http://www.abc.net.au

Jackie from the Home School Learning website has 20 great ideas for educational Melbourne Cup Activities at the following link:

http://www.homeschoollearning.com.au/?p=1698

Here are three of her ideas worth considering for Mathematics Class:

1. Geometry and Design. Take a look at racing colours, each jockey has his/her own unique colours, patterns and design.
What Geometric Shapes and patterns are used. Design you own racing colours.

2. Have a friendly cup sweep at home or with family and friends. It doesn’t matter if you have lots of horses if not many of you are in the sweep that just ups your chance of winning.
Decide on how much money each entry will be there is then calculating of the total. Next how will the prize money be divided. More maths.

3. Distance. The distance is 3200m and which is close to the original 2 miles. Make comparisons to places you go that are 3km away.
Run 100m and discuss that the race is 32 times that distance. Perhaps time your 100m sprint and multiply it out.
Discuss is the resulting time realistic, could you sprint for 3.2km.

4. Get out stopwatches and look at time. The Melbourne Cup is run in around 3 and a half minutes. Time yourselves, hopping, jumping, reading a page what can you do in 3 minutes?

Flash Actionscript Horse Racing Game

If you are interested in Adobe Flash Actionscript Programming, then check out our horse racing game, (with full how to build instructions), at the following link:

http://passyworldofict.blogspot.com.au/2011/04/as-30-horse-race.html

Solving Equations – Onion Skin Methods

Posted on October 27, 2012 by Passy

Image Source: http://s3.amazonaws.com

If trying to solve math equations is driving you to tears, then “The Onion Skin” methods might help make your life a bit easier.

It’s like a pair of goggles that will clear everything up for you, and make you feel happy again!

Passy only discovered this method recently, by seeing a teacher called Nadia, who works with Passy, showing some students how to do this.
(Thanks for sharing this great idea Nadia).

The idea of the method, is that our variable letter is at the center of the onion, and then has skins built onto it by the operations which have been applied to it in the equation.

We then look at peeling back the skins, using reverse operations, to get back to our original variable letter.

Finally we apply these reversing operations to the number value on the right hand side of the equation.

This then gives us a numeric solution to the equation.

Basically it is just another means of doing the “Flowcharts Back-Tracking Method”, and provides a great scaffold for students who are beginners at solving Algebra Equations.

Many “Purists” are not particularly fond of these diagramatical methods. However, here at Passy World we are a firm believer in using diagrams to assist those students who are not yet at a level to work with the abstract “doing to both sides” Algebraic methods.

BODMAS/PEMDAS Order of Operations

Here is a quick review of the Operations we look for when solving Algebra Equations.

For the Equation: 2N + 5 = 11

Operations are + 5 and x2

BODMAS or PEMDAS for these is x2 then + 5

Here are the “Opposite Operations” we need to know when solving Equations.

For our previous example: 2N + 5 = 11

1) Operations are + 5 and x2
2) BODMAS or PEMDAS for these is x2 then + 5
3) Opposites are /2 and -5

Onion Skin Methods for Equations

In this lesson we look at two “Onion Skin” methods for solving Algebra Equations.

The first method uses a flowchart type diagram containing two onions, which we call the “Double Onion Method”.

The second method is a quicker method, that uses only one onion, and is called the “Single Onion Method”.

We recommend starting off using the “”Double Onion Method”, but then upgrading to use the quicker “Single Onion Method” as soon as you are comfortable to do so.

Double Onion Method

The “Double Onion Method” involves drawing two identical onions next to each other, and following through a set of working out steps in a specific order.

The following diagrams show how to work through these steps for the simple equation: n + 5 = 7

If the onion skins have been done correctly, then working outwards from the centre, the operations should be in BODMAS/PEMDAS oder.

Here are the remaining steps of the working out.

Double Onion Two Step Equations

The following diagram shows a fully worked example of using the two onion method for a two step Equation.

Note that the + – x / operations inside the left hand onion should always go from the centre outwards in BODMAS/PEMDAS Order.

The next fully completed example is for a two step equation which contains brackets.

Note that the + – x / operations inside the left hand onion should always go from the centre outwards in BODMAS/PEMDAS Order.

Single Onion Method

The “Single Onion Method” is a quicker method, which uses only one onion.

It is recommended to learn the “Double Onion Method” first, and then progress on to use this single onion method.

The single onion method involves drawing onion rings around the equation which needs to be solved.

These onion skins are created by first drawing a centre skin around the letter variable.

We then create skins outwards from here, following the BODMAS/PEMDAS order of operations.

The outermost skin should enclose the entire equation.

Here is a single onion diagram for our previous example equation:

N + 5 = 7

To solve the Equation, we work from the biggest outer skin, inwards through the smaller skins, applying opposite operations, until we reach the central letter variable.

The following diagram shows our completed equation solution.

Single Onion Method Examples

The following are some fully completed Single Onion Method questions.

They show the onion diagram, followed by the application of the “opposite operations”, to reach the final solution answer.

It is very important when doing the reversing steps, that they are done without a calculator, in the exact order that the “peeling” inwards occurs.

From the onion methods, it should not be too hard to later move to the non-diagram Algebraic working out of equations.

The onions are a handy helper for equations, and generate the reverse order steps, which are essential for solving equations.

The starting onion can be used to work out the reverse operations, and then the normal algebraic operations to both sides steps can be done on the actual equation. The degree to which the diagrams are used is really up to the skill level of the individual student.

Factorising Using an Onion Skin Method

There is also an Onion type method that can be used for finding factors of numbers.

This is demonstrated in the following video.

Boom Crash Opera – Onion Skin

Finally, (for no particular mathematical reason whatsoever), here is one of Passy’s all time favorite songs called “Onion Skin”, by Australian Band “Boom Crash Opera”.

Passy's World of Mathematics

Cost Price Mark Up and Profit

Africa Trip to Ruben Centre

Mathematical Christmas Decorations

Mathematics of the Melbourne Cup

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