Problem Page Try Again an Item on Sale Costs 80% of the Original Price. The Original Price Was $64.
"Percent of" Word Issues:
Markup and Markdown Examples (page 2 of iii)
Sections: Basic pct exercises, Markup / markdown, General increase / decrease
An important category of percentage exercises is markup and markdown problems. For these, you calculate the markup or markdown in absolute terms (yous find past how much the quantity inverse), so y'all summate the percent modify relative to the original value. So they're actually just another form of "increment - subtract" exercises.
- A computer software retailer used a markup rate of 40%. Notice the selling toll of a computer game that cost the retailer $25.
The markup is xl% of the $25 cost, and so the markup is:
(0.40)(25) = ten
So the selling price, being the cost plus markup, is:
25 + 10 = 35
The particular sold for $35.
- A golf store pays its wholesaler $40 for a certain club, and then sells information technology to a golfer for $75 . What is the markup rate?
First, I'll calculate the markup in accented terms:
75 – 40 = 35
Then I'll find the relative markup over the original cost, or the markup rate: ($35) is (some per centum) of ($xl) , or: Copyright © Elizabeth Stapel 1999-2011 All Rights Reserved
35 = (x)(forty)
...so the relative markup over the original price is:
35 ÷ xl = 10 = 0.875
Since ten stands for a percentage, I demand to remember to convert this decimal value to the corresponding pct.
The markup rate is 87.5% .
- A shoe shop uses a 40% markup on cost. Observe the cost of a pair of shoes that sells for $63.
This trouble is somewhat backwards. They gave me the selling price, which is cost plus markup, and they gave me the markup rate, but they didn't tell me the actual cost or markup. Then I have to be clever to solve this.
I will permit " ten " be the toll. Then the markup, being twoscore% of the cost, is 0.xlx . And the selling toll of $63 is the sum of the toll and markup, so:
63 = ten + 0.xlx
63 = aneten + 0.40x
63 = 1.40x
63 ÷ 1.40 = x= 45
The shoes toll the shop $45.
- An detail originally priced at $55 is marked 25% off. What is the sale price?
Beginning, I'll discover the markdown. The markdown is 25% of the original price of $55 , then:
ten = (0.25)(55) = 13.75
By subtracting this markdown from the original cost, I tin find the sale cost:
55 – 13.75 = 41.25
The sale toll is $41.25.
- An item that regularly sells for $425 is marked downward to $318.75 . What is the discount rate?
First, I'll find the amount of the markdown:
425 – 318.75 = 106.25
Then I'll summate "the markdown over the original toll", or the markdown rate: ($106.25) is (some pct) of ($425) , and then:
106.25 = (x)(425)
...and the relative markdown over the original price is:
x = 106.25 ÷ 425 = 0.25
Since the " x " stands for a percentage, I need to retrieve to convert this decimal to percentage course.
The markdown rate is 25%.
- An item is marked downwardly 15% ; the sale price is $127.46 . What was the original price?
This problem is backwards. They gave me the sale toll ($127.46) and the markdown rate (fifteen%) , but neither the markdown amount nor the original cost. I will let " ten " stand for the original price. So the markdown, existence xv% of this cost, was 0.fifteen10 . And the auction price is the original price, less the markdown, so I go:
x – 0.xv10 = 127.46
1x – 0.15x = 127.46
0.85x = 127.46
x = 127.46 ÷ 0.85 = 149.952941176...
This problem didn't land how to round the final respond, but dollars-and-cents is e'er written with two decimal places, and then:
The original price was $149.95.
Note in this terminal problem that I ended up, in the third line of calculations, with an equation that said "eighty-v percent of the original price is $127.46 ". You can save yourself some fourth dimension if y'all think of discounts in this way: if the price is 15% off, then you're only actually paying 85% . Similarly, if the cost is 25% off, then you're paying 75% ; if the price is thirty% off, so you're paying 70% ; and and then on.
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