_8- Percent and Ratio.

Percent and Ratio




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Compound Interest – percent of Inc., Dec. – Tax – discount
P: Start – initial r: rate per ( year – week…. ) t: No. of years- weeks…..
𝑨 = 𝑷(𝟏 ± 𝒓%)𝒕 per year ( week…..)




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𝒓% 𝒏𝒕
𝑨 = 𝑷(𝟏 ± ) every n interval in a year
𝒏
𝒕
𝑨 = 𝑷(𝟏 ± 𝒓%)𝒏 every n years




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𝑻𝒂𝒙 𝒓% 𝒗𝒂𝒍𝒖𝒆 = 𝒑 ( 𝟏 + 𝒓% ) 𝑫𝒊𝒔𝒄 𝒓% 𝒗𝒂𝒍𝒖𝒆 = 𝒑 ( 𝟏 – 𝒓% ) 𝒑 ∶ 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍
Tax n% and discount m% 𝑽𝒂𝒍𝒖𝒆 = 𝒑 ( 𝟏 + 𝒏% ) ( 𝟏 – 𝒎% )
(𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 )
P𝒆𝒓𝒄𝒆𝒏𝒕 𝒐𝒇 𝑰𝒏𝒄. (𝑫𝒆𝒄. ) = × 𝟏𝟎𝟎%
𝒐𝒍𝒅




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Ratio and compound of two ratios:
𝒂
𝒃
= 𝒂: 𝒃

ex: a : b = 2:3 a :b : sum
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𝟐 𝟑
2 :3 : 5 a = of total b= of total
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𝟓 𝟓

Ex: a : b : c = 1 : 2 : 4 a : b : c : sum
𝟏 𝟐 𝟒
1 2 4 7 a = 𝟕x total b= 𝟕 x total c= 𝟕
x total
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Ex: a : b = 3 : 2 , b:c =5:2 a : c = ??

a: b:c

3 :2

5 : 2
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15 : 10 : 4 a : c = 15 : 4

Ex: a : b = 2 : 5 , a:c=5:3 b : c ?? a :b :c
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2 :5

5 :3
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____________

10: 25: 6 b : c = 25 : 6
AmrBoard SAT Helper - Percent and Ratio 1
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, 1 AmrBoard SAT Helper 2 AmrBoard SAT Helper


When Shondra makes an online purchase, a 15% The Lees have budgeted between $200,000 and




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Discount is applied to the retail price and then a $300,000 for their new home. Approximately what
6.25% tax is added to this discounted price. Which of the percentage of the houses shown in the graph are priced
following represents the amount Shondra pays, in dollars, for within the range of this budget?




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an item with a retail price of x dollars?

A) x - 0.15 + 0.0625x
A) 35%
B) 1.0625x - 0. 15x
B) 40%




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C) 1.0625(0.85x)
C) 45%
D) x - 0.15 ( 1.0625x )
D) 55%



3 AmrBoard SAT Helper




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The line of best fit for these data has the equation

y = 0.12x + 3.37, where x represents the total square


Questions 2 - 3refer to the following information.
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footage of the house, and y represents the selling price,
in thousands of dollars, for the house. Which choice
best describes the meaning of the number 0.12 in this
TM
equation?

A) The selling price of the smallest house in the area is
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about $1,200.

B) The average selling price of a house, in thousands of
dollars, is about 12% of the size of the house in

The scatterplot above shows the selling price and area, in square feet.
square feet, for 20 homes in a suburban area, as well as
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the line of best fit for the data. C) For every increase of 1 square foot in the size of the
house, the average selling price increases by about
$120.
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D) For every increase of 1 square foot in the size of the
house, its average selling price increases by about
$0.12.
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AmrBoard SAT Helper - Percent and Ratio 2
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, 4 AmrBoard SAT Helper 6 AmrBoard SAT Helper


Approximately 3 million U.S. students graduated from Light travels through a vacuum at a speed of




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high school in 2014, and of those, 70% of the women approximately 186,000 miles per second.
and 65% of the men enrolled in college. The U.S. school Approximately how many miles will a ray of light
population is approximately 49% male and 51% female.
travel through a vacuum in one day?




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Which of the following is the best estimate of the
A) 6.7 x 108 miles
number of 2014 female high school graduates who did
B) 1.6 x 1010 miles
not enroll in college?
C) 3.2 x 1010 miles




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A) 459,000
D) 4.6 x 1013 miles
B) 509,000

C) 907,000

D) 1,080,000




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AT
TM
5 AmrBoard SAT Helper


In a poll of n students at a local college, 45% of these
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students identify themselves as liberals. Of these,
60% support universal health care. If 405 students
of these students are liberals who support universal
health care, what is the value of n ?
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A) 109
B) 675
C) 900
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D) 1,500
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AmrBoard SAT Helper - Percent and Ratio 3
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