Solving algebra problems about markup
What is markup?
In this lesson we will learn how to calculate a percent markup and how it changes the original price of an item.
What is a percent markup? Well in retail, a store will buy an item for a certain amount from a manufacturer. In order to make money the store has to add to the price they paid for it and sell it to the customer for more.
The store usually does this a percentage of the original amount, and if that’s the case we call this a percent markup.
Here are two different formulas we can use to describe this:
???\text{New Price} = \text{Original Price} + \text{Markup Amount}???
???\text{New Price}=\text{Original Price}\left(1 + \frac{\text{Percent Markup}}{100}\right)???
???\text{Markup Amount} =\text{Original Price} \left(\frac{\text{Percent Markup}}{100}\right)???
In this formula, “New Price” is what the end customer pays the store for the item. The New Price of an item is often called the “Selling Price”.
“Original Price” is what the store paid the manufacturer for the item. This is sometimes called the “Manufacturer’s Price” or the “Original Purchase Price”.
“Percent Markup” is the percentage of the “Original Price” by which the store marked up the item in order to get to the “New Price”.
How to calculate markup
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Using markup to find selling price
Example
A used car store manager purchases a used car for ???\$13,500.00???. The percent markup on the car is ???45\%???. What is the selling price of the car?
First, we’ll find the amount of money the company added to the original price of the car. We’ll multiply ???45\%??? by the original amount of the car.
???45\% \cdot \$13,500???
???\frac{45}{100} \cdot \$13,500???
???\$6,075???
This means the company marked the original price up by ???\$6,075???, so now we need to add this to the original price to find the selling price.
???\$13,500 + \$6,075???
???\$19,575???
Let’s look at an example on how to find the manufacturer’s price.
Example
A bakery purchases a set of pre-made cakes from the manufacturer and sells them to their customers for ???\$545.82???. The markup was ???65\%???. What was the original price of the cakes that the bakery paid to the manufacturer?
If the bakery paid ???x??? for the cakes and marked them up by ???65\%???, then the price they’re selling it to their customers for is ???1.65??? times the price they paid for it.
???1.65x = \$545.82???
???\frac{1.65x}{1.65} = \frac{\$545.82}{1.65}???
???x = \$330.80???
The bakery paid ???\$330.80??? for the cakes, marked them up by ???65\%???, which was a markup of ???\$215.02???, and then sold them to their customers for a total of ???\$330.80+\$215.02=\$545.82???.