Percent – Base and rate Problems You might know the “base / rate” problems as “is / of”...
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![Page 1: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/1.jpg)
Percent – Base and rate Problems
You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?
![Page 2: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/2.jpg)
Percent – Base and rate Problems
You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?
Every one of these problems can be set up with the same format.
100%
ofis
![Page 3: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/3.jpg)
Percent – Base and rate Problems
You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?
Every one of these problems can be set up with the same format :
100%
ofis
To set up the problem, go thru the given information and insert known values into the format…
100%
ofis
![Page 4: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/4.jpg)
Percent – Base and rate Problems
You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?
Every one of these problems can be set up with the same format :
100%
ofis
To set up the problem, go thru the given information and insert known values into the format…
In our example above…23 is what percent of 50
100%
of23
![Page 5: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/5.jpg)
Percent – Base and rate Problems
You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?
Every one of these problems can be set up with the same format :
100%
ofis
To set up the problem, go thru the given information and insert known values into the format…
In our example above…23 is what percent of 50
100%
5023
![Page 6: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/6.jpg)
Percent – Base and rate Problems
You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?
Every one of these problems can be set up with the same format :
100%
ofis
To set up the problem, go thru the given information and insert known values into the format…
In our example above…23 is what percent of 50
100%
5023
It’s now a basic proportion and you find what is missing…in this case %
![Page 7: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/7.jpg)
Percent – Base and rate Problems
You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?
100%
5023
A short cut for solving proportions, one that gets all the Algebra OUT is this :1. Begin with the partner of the unknown ( red box )2. Move around the outside the proportion ( green box )3. Divide, then multiply to get the unknown
Divide
Multiply
![Page 8: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/8.jpg)
Percent – Base and rate Problems
You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?
100%
5023
A short cut for solving proportions, one that gets all the Algebra OUT is this :1. Begin with the partner of the unknown ( red box )2. Move around the outside the proportion ( green box )3. Divide, then multiply to get the unknown
Divide
Multiply
%462322350100
![Page 9: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/9.jpg)
Percent – Base and rate Problems
EXAMPLE # 2 : What is 35 % of 80
![Page 10: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/10.jpg)
Percent – Base and rate Problems
EXAMPLE # 2 : What is 35 % of 80
100%
ofis
![Page 11: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/11.jpg)
Percent – Base and rate Problems
EXAMPLE # 2 : What is 35 % of 80
10035
80is
100%
ofis
![Page 12: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/12.jpg)
Percent – Base and rate Problems
EXAMPLE # 2 : What is 35 % of 80
10035
80is
100%
ofis
Divide
Multiply
28358.03510080
![Page 13: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/13.jpg)
Percent – Base and rate Problems
EXAMPLE # 3 : 15 is 20 % of what number
100%
ofis
![Page 14: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/14.jpg)
Percent – Base and rate Problems
EXAMPLE # 3 : 15 is 20 % of what number
10020
of15
100%
ofis
Divide
Multiply
7510075.01002015
![Page 15: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/15.jpg)
APPLICATION PROBLEMS
In most percent application problems, you have to determine what the problem is asking for and then use the is / of proportion to solve.
![Page 16: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/16.jpg)
APPLICATION PROBLEMS
In most percent application problems, you have to determine what the problem is asking for and then use the is / of proportion to solve.
EXAMPLE : And inspector rejects 12 out of 250 parts due to being out of tolerance. What percentage of parts were rejected ?
![Page 17: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/17.jpg)
APPLICATION PROBLEMS
In most percent application problems, you have to determine what the problem is asking for and then use the is / of proportion to solve.
EXAMPLE : And inspector rejects 12 out of 250 parts due to being out of tolerance. What percentage of parts were rejected ?SOLUTION :
What is the problem asking us to find ?
![Page 18: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/18.jpg)
APPLICATION PROBLEMS
In most percent application problems, you have to determine what the problem is asking for and then use the is / of proportion to solve.
EXAMPLE : And inspector rejects 12 out of 250 parts due to being out of tolerance. What percentage of parts were rejected ?SOLUTION :
What is the problem asking us to find ?The problem is asking for the % of rejects, so the “is” and “of” part is in the wording somewhere.
![Page 19: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/19.jpg)
APPLICATION PROBLEMS
In most percent application problems, you have to determine what the problem is asking for and then use the is / of proportion to solve.
EXAMPLE : And inspector rejects 12 out of 250 parts due to being out of tolerance. What percentage of parts were rejected ?SOLUTION :
What is the problem asking us to find ?The problem is asking for the % of rejects, so the “is” and “of” part is in the wording somewhere.
I can see the “of” easily…
![Page 20: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/20.jpg)
APPLICATION PROBLEMS
In most percent application problems, you have to determine what the problem is asking for and then use the is / of proportion to solve.
EXAMPLE : And inspector rejects 12 out of 250 parts due to being out of tolerance. What percentage of parts were rejected ?SOLUTION :
What is the problem asking us to find ?The problem is asking for the % of rejects, so the “is” and “of” part is in the wording somewhere.
I can see the “of” easily…Which leaves the 12 as the “is”…
![Page 21: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/21.jpg)
APPLICATION PROBLEMS
In most percent application problems, you have to determine what the problem is asking for and then use the is / of proportion to solve.
EXAMPLE : And inspector rejects 12 out of 250 parts due to being out of tolerance. What percentage of parts were rejected ?SOLUTION :
What is the problem asking us to find ?The problem is asking for the % of rejects, so the “is” and “of” part is in the wording somewhere.
I can see the “of” easily…Which leaves the 12 as the “is”…
Now just solve like we did before…
Divide
Multiply
100÷250×12=4.8 %
![Page 22: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/22.jpg)
APPLICATION PROBLEMS
EXAMPLE #2 :A motor is said to be 80% efficient if the output power delivered is 80% of the input power received. How many horsepower does a motor have if it is 80% efficient with a 6.20 horsepower output.
![Page 23: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/23.jpg)
APPLICATION PROBLEMS
EXAMPLE #2 :A motor is said to be 80% efficient if the output power delivered is 80% of the input power received. How many horsepower does a motor have if it is 80% efficient with a 6.20 horsepower output.
SOLUTION :
Again we can quickly identify one part of the proportion… 80 % goes in the “%” spot.
![Page 24: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/24.jpg)
APPLICATION PROBLEMS
EXAMPLE #2 :A motor is said to be 80% efficient if the output power delivered is 80% of the input power received. How many horsepower does a motor have if it is 80% efficient with a 6.20 horsepower output.
SOLUTION :
Again we can quickly identify one part of the proportion… 80 % goes in the “%” spot.
Since the motor IS 80% efficient, the known output ( 6.20 hp ) goes in the “is” spot…
![Page 25: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/25.jpg)
APPLICATION PROBLEMS
EXAMPLE #2 :A motor is said to be 80% efficient if the output power delivered is 80% of the input power received. How many horsepower does a motor have if it is 80% efficient with a 6.20 horsepower output.
SOLUTION :
Again we can quickly identify one part of the proportion… 80 % goes in the “%” spot.
Since the motor IS 80% efficient, the known output ( 6.20 hp ) goes in the “is” spot…
Once again follow the rules for solving the unknown …
![Page 26: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/26.jpg)
APPLICATION PROBLEMS
EXAMPLE #3 :By replacing high – speed cutters with carbide cutters, a machinist increases productivity by 35%. Using carbide cutters, 270 pieces per day are produced. How many pieces per day were produced by the steel cutters ?
![Page 27: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/27.jpg)
APPLICATION PROBLEMS
EXAMPLE #3 :By replacing high – speed cutters with carbide cutters, a machinist increases productivity by 35%. Using carbide cutters, 270 pieces per day are produced. How many pieces per day were produced by the steel cutters ?
SOLUTION : 𝑖𝑠𝑜𝑓 =
%100
![Page 28: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/28.jpg)
APPLICATION PROBLEMS
EXAMPLE #3 :By replacing high – speed cutters with carbide cutters, a machinist increases productivity by 35%. Using carbide cutters, 270 pieces per day are produced. How many pieces per day were produced by the steel cutters ?
SOLUTION : 𝑖𝑠𝑜𝑓 =
135100
When production increases or decreases, the beginning percent is always 100%. An increase will add to the 100%, a decrease will subtract from the 100%. Since production increased by 35%, our new production rate is
100% + 35% = 135%.
![Page 29: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/29.jpg)
APPLICATION PROBLEMS
EXAMPLE #3 :By replacing high – speed cutters with carbide cutters, a machinist increases productivity by 35%. Using carbide cutters, 270 pieces per day are produced. How many pieces per day were produced by the steel cutters ?
SOLUTION : 270𝑜𝑓 =
135100
When production increases or decreases, the beginning percent is always 100%. An increase will add to the 100%, a decrease will subtract from the 100%. Since production increased by 35%, our new production rate is
100% + 35% = 135%.
The new number of pieces is a result of the increase or decrease in production and must be placed in the proportion relative to the increase or decrease.
![Page 30: Percent – Base and rate Problems You might know the “base / rate” problems as “is / of” problems. For example, 23 is what percent of 50 ?](https://reader036.fdocuments.in/reader036/viewer/2022062412/5a4d1b0f7f8b9ab05998e17e/html5/thumbnails/30.jpg)
APPLICATION PROBLEMS
EXAMPLE #3 :By replacing high – speed cutters with carbide cutters, a machinist increases productivity by 35%. Using carbide cutters, 270 pieces per day are produced. How many pieces per day were produced by the steel cutters ?
SOLUTION : 270𝑜𝑓 =
135100
When production increases or decreases, the beginning percent is always 100%. An increase will add to the 100%, a decrease will subtract from the 100%. Since production increased by 35%, our new production rate is
100% + 35% = 135%.
The new number of pieces is a result of the increase or decrease in production and must be placed in the proportion relative to the increase or decrease.
Solve for unknown :