How to find the whole from the part with percentage - ISEE Middle Level Quantitative Reasoning
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Refer to the above diagram. If there were 15,934 voters who were affiliated with a political party in Smith County in 2009, how many voters (nearest whole number) were there total?
Refer to the above diagram. If there were 15,934 voters who were affiliated with a political party in Smith County in 2009, how many voters (nearest whole number) were there total?
40% of the voters were registered as independents, so 60% were registered as a member of a political party. Since 60% of the voters numbered 15,934, we can find the total number of voters by setting up and solving a proportion:
which rounds to 26,557 voters.
40% of the voters were registered as independents, so 60% were registered as a member of a political party. Since 60% of the voters numbered 15,934, we can find the total number of voters by setting up and solving a proportion:
which rounds to 26,557 voters.
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Refer to the above graph. If there were 17,856 registered voters in Smith County in 2009, how many voters were registered as neither Republicans nor Democrats (nearest whole number)?
Refer to the above graph. If there were 17,856 registered voters in Smith County in 2009, how many voters were registered as neither Republicans nor Democrats (nearest whole number)?
2% of the voters were registered as members of other parties, and 40% were unaffiliated, so we want to calculate 42% of 17,856, or, equivalently,
which, to the nearest whole number, rounds to 7,500 voters.
2% of the voters were registered as members of other parties, and 40% were unaffiliated, so we want to calculate 42% of 17,856, or, equivalently,
which, to the nearest whole number, rounds to 7,500 voters.
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If sales tax on a pair of jeans is 
, and the jeans cost 
before tax, what is the final price of the jeans including tax?
If sales tax on a pair of jeans is
Since the jeans are the only item being purchased, and they cost $
, we must first find 
% of $
. In order to do that we multiply $
by the decimal form of 
%, which is 
.
Note: In order to find the decimal form of a percent, we divide it by 
. 
Find the tax:
Therefore the sales tax added to the original price is $
.
The final cost of the jeans is $
.
Since the jeans are the only item being purchased, and they cost $
Note: In order to find the decimal form of a percent, we divide it by
Find the tax:
Therefore the sales tax added to the original price is $
The final cost of the jeans is $
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For her birthday, Susan asks her mother to buy her a car. Susan’s mother agrees to give Susan 150 percent of whatever amount Susan can save up in six months. If Susan saves 
, how much does Susan’s mother owe her?
For her birthday, Susan asks her mother to buy her a car. Susan’s mother agrees to give Susan 150 percent of whatever amount Susan can save up in six months. If Susan saves
When Susan's mother agreed to match her savings plus fifty percent, she agreed to give Susan 
% plus 
%.
Before multiplying by the amount Susan saved, we must convert 
% to a decimal by dividing by 
.
Now we multiply 
time $
.
Susan's mother owes her $
.
When Susan's mother agreed to match her savings plus fifty percent, she agreed to give Susan
Before multiplying by the amount Susan saved, we must convert
Now we multiply
Susan's mother owes her $
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240 is 30% of what number?
240 is 30% of what number?
Set up the proportion statement and solve for 
:
Cross-multiply:
Set up the proportion statement and solve for
Cross-multiply:
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420 is 150% of what number?
420 is 150% of what number?
Set up the proportion statement and solve for 
by cross-multiplying:
Set up the proportion statement and solve for
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70 is 
of what number?
70 is
Set up the proportion statement and solve for 
by cross-multiplying:
Set up the proportion statement and solve for
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24 is 25% of what number?
24 is 25% of what number?
Think 
is 
of 
.
So:
and 
.
We have:
Think
So:
We have:
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Julie bought some groceries at the store where she works for $196.57. She got an employee discount of 15%. How much would the same groceries cost a non-employee?
Julie bought some groceries at the store where she works for $196.57. She got an employee discount of 15%. How much would the same groceries cost a non-employee?
Paying at a 15% discount is equvalent to paying 85% of the original price, so $196.57 is 85% of the original (non-employee) price, or, equivalently, 0.85 times that price. If 
is that price, then we can set up and solve the equation:
A non-employee would pay $231.26 for the groceries.
Paying at a 15% discount is equvalent to paying 85% of the original price, so $196.57 is 85% of the original (non-employee) price, or, equivalently, 0.85 times that price. If
A non-employee would pay $231.26 for the groceries.
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Becky ate 
of a batch of cupcakes. She ate 
cupcakes. How many cupcakes were there in total?
Becky ate
This can be solved using a proportion:
Cross multiply and solve for 
:
This can be solved using a proportion:
Cross multiply and solve for
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At a pet store, there are 12 dogs and 8 cats. The following week, the number of dogs increases by 25%, while the number of cats decreases by 25%. What is the total number of animals at the store the following week?
Assume the store only sells dogs and cats.
At a pet store, there are 12 dogs and 8 cats. The following week, the number of dogs increases by 25%, while the number of cats decreases by 25%. What is the total number of animals at the store the following week?
Assume the store only sells dogs and cats.
If the population of dogs increases by 25%, then we first find 25% of 12 (which is 3) and add the 3 to 12. This gives us 15 dogs.
If the population of cats decreases by 25%, then we find 25% of 8 (which is 2), and subtract if from 8. This gives us 6.
Now that we know the final individual numbers of dogs and cats, we can add them to find the final answer.
If the population of dogs increases by 25%, then we first find 25% of 12 (which is 3) and add the 3 to 12. This gives us 15 dogs.
If the population of cats decreases by 25%, then we find 25% of 8 (which is 2), and subtract if from 8. This gives us 6.
Now that we know the final individual numbers of dogs and cats, we can add them to find the final answer.
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10 percent of a cake weights 20 ounces. The entire cake is cut into 8 pieces. How many ounces does each piece weigh?
10 percent of a cake weights 20 ounces. The entire cake is cut into 8 pieces. How many ounces does each piece weigh?
If 10 percent of the cake weights 20 ounces, then the entire cake will weigh 200 ounces, because 10 times 20 is 200.
If the cake has 8 slices, then each slice will weigh (in ounces) 200 divided by 8. 200 divided by 8 is 25; therefore, 25 ounces is the correct answer.
If 10 percent of the cake weights 20 ounces, then the entire cake will weigh 200 ounces, because 10 times 20 is 200.
If the cake has 8 slices, then each slice will weigh (in ounces) 200 divided by 8. 200 divided by 8 is 25; therefore, 25 ounces is the correct answer.
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Tom the baker made 
blueberry muffins on Tuesday, and Stan the baker made and 
muffins that day. On Wednesday, each baker decided to increase his production of blueberry muffins by 
. What is the average of blueberry muffins that Tom and Stan baked on Wednesday?
Tom the baker made
Tom made 
blueberry muffins on Tuesday, and Stan made and 
muffins that day. On Wednesday, each baker decided to increase his production of blueberry muffins by 
.
Given that 
of 
is 
, the number of muffins made by Tom on Wednesday would be 
.
Given that 
of 
is 
, the number of muffins made by Stan on Wednesday would be 
.
The average is calculated by adding numbers in a list together, and then dividing by the number of items in that list. This gives us:
Tom made
Given that
Given that
The average is calculated by adding numbers in a list together, and then dividing by the number of items in that list. This gives us:
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There are 12 sopranos in the Red Street Choir. If sopranos are 40% of the choir, how many total members make up the Red Street Choir?
There are 12 sopranos in the Red Street Choir. If sopranos are 40% of the choir, how many total members make up the Red Street Choir?
When given a part, you can use a percentage to determine the whole by converting the percentage to a decimal and dividing the part by that number.
When given a part, you can use a percentage to determine the whole by converting the percentage to a decimal and dividing the part by that number.
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If you have 
of a quiz completed after 
questions, how long is the quiz?
If you have
To find a part of a whole with a percentage, you multiply the whole by the percent.
To find the opposite, you divide the part by the percent so it would be 
.
This is equal to
or 
.
To find a part of a whole with a percentage, you multiply the whole by the percent.
To find the opposite, you divide the part by the percent so it would be
This is equal to
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There are 8 pieces of pizza. If Justin at 25% of the pizza, how many pieces did he have?
There are 8 pieces of pizza. If Justin at 25% of the pizza, how many pieces did he have?
25% is equivalent to the fraction
and can then be reduced to
which is equivalent to
,
meaning that if Justin ate 25% of the pizza, he ate 2 of the 8 pieces.
25% is equivalent to the fraction
meaning that if Justin ate 25% of the pizza, he ate 2 of the 8 pieces.
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Refer to the above diagram. If there were 15,934 voters who were affiliated with a political party in Smith County in 2009, how many voters (nearest whole number) were there total?
Refer to the above diagram. If there were 15,934 voters who were affiliated with a political party in Smith County in 2009, how many voters (nearest whole number) were there total?
40% of the voters were registered as independents, so 60% were registered as a member of a political party. Since 60% of the voters numbered 15,934, we can find the total number of voters by setting up and solving a proportion:
which rounds to 26,557 voters.
40% of the voters were registered as independents, so 60% were registered as a member of a political party. Since 60% of the voters numbered 15,934, we can find the total number of voters by setting up and solving a proportion:
which rounds to 26,557 voters.
Compare your answer with the correct one above
Refer to the above graph. If there were 17,856 registered voters in Smith County in 2009, how many voters were registered as neither Republicans nor Democrats (nearest whole number)?
Refer to the above graph. If there were 17,856 registered voters in Smith County in 2009, how many voters were registered as neither Republicans nor Democrats (nearest whole number)?
2% of the voters were registered as members of other parties, and 40% were unaffiliated, so we want to calculate 42% of 17,856, or, equivalently,
which, to the nearest whole number, rounds to 7,500 voters.
2% of the voters were registered as members of other parties, and 40% were unaffiliated, so we want to calculate 42% of 17,856, or, equivalently,
which, to the nearest whole number, rounds to 7,500 voters.
Compare your answer with the correct one above
If sales tax on a pair of jeans is , and the jeans cost before tax, what is the final price of the jeans including tax?
If sales tax on a pair of jeans is
Since the jeans are the only item being purchased, and they cost $, we must first find % of $. In order to do that we multiply $ by the decimal form of %, which is .
Note: In order to find the decimal form of a percent, we divide it by .
Find the tax:
Therefore the sales tax added to the original price is $.
The final cost of the jeans is $.
Since the jeans are the only item being purchased, and they cost $
Note: In order to find the decimal form of a percent, we divide it by
Find the tax:
Therefore the sales tax added to the original price is $
The final cost of the jeans is $
Compare your answer with the correct one above
For her birthday, Susan asks her mother to buy her a car. Susan’s mother agrees to give Susan 150 percent of whatever amount Susan can save up in six months. If Susan saves , how much does Susan’s mother owe her?
For her birthday, Susan asks her mother to buy her a car. Susan’s mother agrees to give Susan 150 percent of whatever amount Susan can save up in six months. If Susan saves
When Susan's mother agreed to match her savings plus fifty percent, she agreed to give Susan % plus %.
Before multiplying by the amount Susan saved, we must convert % to a decimal by dividing by .
Now we multiply time $.
Susan's mother owes her $.
When Susan's mother agreed to match her savings plus fifty percent, she agreed to give Susan
Before multiplying by the amount Susan saved, we must convert
Now we multiply
Susan's mother owes her $
Compare your answer with the correct one above