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"Percent of" Word Problems:
     Markup and Markdown Examples (page 2 of 3)

Sections: Basic percentage exercises, Markup / markdown, General increase / decrease

An important category of percentage problems is markup-markdown problems. For these, you calculate the markup or markdown in absolute terms (that is, you determine by what number the original quantity changed), and then you calculate the percent change relative to the original value.

• A computer software retailer used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25.

The markup is 40% of the cost, so the markup is:

(0.40)(25) = 10

Then the selling price, being the cost plus markup, is:

25 + 10 = 35

The item sold for $35.

• A golf shop pays its wholesaler $40 for a certain club, and then sells it for $75. What is the markup rate?

First, I'll calculate the markup in absolute terms:

75 – 40 = 35

Then I'll find the relative markup over the original price, or the markup rate: ($35) is (some percent) of ($40), or:

35 = (x)(40)

...so the relative markup over the original price is: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

³⁵/₄₀ = x = 0.875

Since x stands for a percentage, I need to remember to convert this decimal value to a percent.

The markup rate is 87.5%.

• A shoe store uses a 40% markup on cost. Find the cost of a pair of shoes that sells for $63.

This problem is kinda backwards. They gave me the selling price, which is cost plus markup, and the markup rate, but not the actual cost or markup. So I have to be clever to solve this. Let "x" be the cost. Then the markup is 0.40x. And the selling price of $63 is the sum of the cost and markup, so:   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

63 = x + 0.40x
63 = 1x + 0.40x
63 = 1.40x
⁶³/_1.40 = x= 45

The shoes cost the store $45.

• An item originally priced at $55 is marked 25% off. What is the sale price?

First, I'll find the markdown. The markdown is 25% of the original value, so:

x = (0.25)(55) = 13.75

Then I'll calculate the sale price, by subtracting the markdown from the original price:

55 – 13.75 = 41.25

The sale price is $41.25.

• An item that regularly sells for $425 is marked down to $318.75. What is the discount rate?

First, find the markdown:

425 – 318.75 = 106.25

Then I calculate the markdown over the original price, or markdown rate: ($106.25) is (some percent) of ($425), so:

106.25 = (x)(425)

...and the relative markdown over the original price is:

x = ^106.25/₄₂₅ = 0.25

Since "x" stands for a percentage, I need to remember to convert this decimal to a percent.

The markdown rate is 25%.

• An item is marked down 15%; the sale price is $127.46. What was the original price?

This problem is backwards. They gave me the sale price ($127.46) and the markdown rate (15%), but neither the markdown nor the original price. Let "x" be the original price. Then the markdown was 0.15x. And the sale price is the original price, less the markdown, so we get:

x – 0.15x = 127.46
1x – 0.15x = 127.46
0.85x = 127.46
x = ^127.46/_0.85 = 149.952941176...

This problem didn't state how to round the final answer, but dollars-and-cents is always written with two decimal places, so:

The original price was $149.95.

Note in this last problem that we ended up, in the third line of calculations, with an equation that said "eighty-five percent of the original price is $127.46". You can save yourself some time if you think of discounts in this way: if the price is 15% off, then you're only actually paying 85%. Similarly, if the price is 25% off, then you're paying 75%; if the price is 30% off, then you're paying 70%; and so on.

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