Welcome!
In this video, we discuss the relationship between selling price, cost and markup, with
examples.
Markup simply refers to the difference between what an item was purchased for an what it
was sold for.
That is, Markup = Selling Price – Cost.
Or M (for markup) = S (for selling price) minus C (for cost)
So, if you buy a watch for $10 and sell it for $15, your markup is $5.
Markup can also be seen as the amount you add to the cost of an item before selling
it.
That is, Selling Price = Cost + Markup.
So, for the watch that costs you $10 to buy, you add $5 on top and sell it for $15.
And that also means, Cost = Selling Price minus Markup.
Thus, Selling Price = Cost + Markup
Cost = Selling Price – Markup And Markup = Selling Price - Cost
Now, some businesses calculate their markup as a percent of cost while some calculate
it as a percent of selling price.
The rate of markup based on Cost, which we denote
RC is Markup divided by Cost.
And the rate of markup based on selling price, which we denote
RS is Markup divided by Selling Price.
And we often multiply these by 100% to convert them from decimal to percent.
So, if Markup is 60% of cost, for example, we write M = 0.6C.
And if Markup is given as 45% of Selling Price, we write M = 0.45S
Now, let’s solve some problems:
In number 1, a store sells a nail trimmer for $12.00 after adding a $6.40 markup.
In part a), we want the unit cost, which is selling price minus markup.
And that will be 12 – 6.4 which gives $5.60.
The rate of markup based on cost is therefore, 6.4 divided by 5.6.
And that will give 1.143 which when multiplied by 100% gives 114.3%.
In #2, we have a power bank that costs $18 and is marked up 40% of cost.
That is, the rate of markup based on cost is 40%, or
Markup is 0.4 times Cost.
Since cost is $18, then the amount of markup is 0.4 times 18, which gives $7.20.
The selling price can thus be found by adding cost and markup.
And that gives $25.20.
Let’s now calculate the missing values in this cost-markup-selling-price table.
In part a), we have a cost of $70 and the rate of markup based on selling price is 60%.
That is, markup is 0.6 of selling price.
Beginning with the formula, Selling Price = Cost + Markup, we have
S = 70 + 0.6S We can then solve for S by first bringing
0.6S to the left of the equal sign.
And we have S (or 1S) minus 0.6S equals 70.
That is, 0.4S equals 70.
So, dividing both sides by 0.4, the selling price will be $175.
We can then calculate the markup as selling price minus cost, which gives $105.
The rate of markup on cost is therefore markup divided by cost, which gives 1.5.
And that is 150%, not 1.5%.
In b), we have a selling price of 57.60 and rate of markup based on cost of 28%.
That is, Markup is 28% of cost or M = 0.28 C
So, from Selling Price = Cost + Markup, we have
57.6 =1C + 0.28C. So, 57.6 = 1.28C
And dividing both sides by 1.28 gives the Cost price of $45.
Now, the amount of markup is selling price minus cost, which is $12.6 .
The rate of markup based on selling price is therefore markup over selling price which
gives 0.2188 or 21.88%.
In part c), we have a markup of $270 and a rate of markup based on selling price of 37.5%.
That is, Markup = .375S
Or 270 = 0.375S
Dividing both sides by 0.375, we have a selling price of $720.
Cost is therefore Selling Price minus Markup which is $450.
And finally, the rate of markup based on cost is 270/450 which is 0.6 or 60%.
In the next video we will break markup into Expenses and Profit, and solve related problems.
Thanks for watching.