Solving percent markdown problems
What are percent markdown problems?
In this lesson we’ll learn how to calculate a percent of, and the new sale price of an item with a discount.
What is a percent markdown? In retail, a store will discount an item in order to sell it more quickly. The store usually does this as a percentage off the original amount they had planned to charge, and if that’s the case we call this a percent markdown.
Here are a few formulas for a discount price after a markdown:
???\text{Discount Price} = \text{Original Price} - \text{Discount Amount}???
???\text{Discount Price}=\text{Original Price}\left(1-\frac{\text{Percent Markdown}}{100}\right)???
???\text{Discount Amount}=\text{Original Price}\left(\frac{\text{Percent Markdown}}{100}\right)???
A useful proportion:
???\frac{\text{Discount Amount}}{\text{Original Price}} = \frac{\text{Percent Markdown}}{100}???
The Percent Markdown is the percentage off the item, sometimes we say the item is on sale for ___% off.
The Original Price (regular price) is what the person or store was selling the item for before the discount.
The Discount Amount is the amount in dollars that is taken off the original price.
The Sale Price is the current selling price of the item after the discount.
How to solve every kind of percent markdown problem
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A few percent markdown examples
Example
A shirt has an original price of ???\$25.00???, and it’s now on sale for ???\$22.50???. What is the percent markdown?
Here’s what we know:
Original Price: ???\$25.00???
Sale Price: ???\$22.50???
We can find the discount amount:
???\$25.00-\$22.50=\$2.50???
Now use the formula:
???\frac{\text{Discount Amount}}{\text{Original Price}} = \frac{\text{Percent Markdown}}{100}???
???\frac{2.5}{25}=\frac{x}{100}???
???\frac{2.5 \cdot 4}{25 \cdot 4}=\frac{x}{100}???
???\frac{10}{100}=\frac{x}{100}???
???x=10???
The percent markdown is ???10\%???.
Let’s look at another example.
Example
A doll has an original price of ???\$22.00???, but it’s on sale for ???\$16.50???. What is the percent markdown?
A doll was originally ???\$22.00??? but the price is now reduced by ???\$5.50??? down to ???\$16.50???. Use the proportion:
???\frac{\text{Discount Amount}}{\text{Original Price}} = \frac{\text{Percent Markdown}}{100}???
???\frac{5.5}{22}=\frac{x}{100}???
???100\cdot \frac{5.5}{22}=x???
???\frac{550}{22} = x???
???x=25\%???
The percent markdown is ???25\%???.
Let’s look at a final example on calculating the sale price.
Example
The regular price of an item is ???\$150.00??? the item is on clearance for ???75\%??? off the regular price. What is the sale price of the item?
The item was originally ???\$150.00???, but the price is reduced by ???75\%???, which means we need to figure out what ???75\%??? of ???\$150.00??? is and then subtract that from the regular price.
???\$150.00 \cdot 75\%???
???\$150 \cdot 75\%???
???\$112.50???
That means that once we take off that amount, the sale price of the item is
???\$150.00 - \$112.50???
???\$37.50???