How to find the whole from the part with percentage - Algebra
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70% of a quantity is 35. What is the quantity?
70% of a quantity is 35. What is the quantity?
We can write this as an equation:
We can write this as an equation:
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80% of ____ = 72?
80% of ____ = 72?
Divide by fractions:
Divide by fractions:
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If 45 is 15% of 
, find the value of 
.
If 45 is 15% of
The key to this problem is identifying that "15% of 
" is the same as 
. With this information, we can write out the simple equation
Dividing both sides by 
gives us
The key to this problem is identifying that "15% of
Dividing both sides by
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In a classroom survey, 18 kids reported having brown hair. The teacher calculated that the 18 with brown hair make up 60% of her class. How many total students are in the class?
In a classroom survey, 18 kids reported having brown hair. The teacher calculated that the 18 with brown hair make up 60% of her class. How many total students are in the class?
Set up an equation representing the information you are given to start (18 out of an unknown total equals 60% or 60 out of 100).
Manipulate the equation to get X by itself.
There are 30 total students in the class.
Set up an equation representing the information you are given to start (18 out of an unknown total equals 60% or 60 out of 100).
Manipulate the equation to get X by itself.
There are 30 total students in the class.
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Malcolm spent 15% of his money on a bicycle that costs $300. How many dollars does Malcolm have left?
Malcolm spent 15% of his money on a bicycle that costs $300. How many dollars does Malcolm have left?
If $300 was 15% of Malcolm's money, then we can figure out how much money Malcolm had by creating this equation:
In this case, Malcolm had $2,000. Since he spent $300 of it on a bicycle, he has only $1,700 left.
If $300 was 15% of Malcolm's money, then we can figure out how much money Malcolm had by creating this equation:
In this case, Malcolm had $2,000. Since he spent $300 of it on a bicycle, he has only $1,700 left.
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Dana spent 24% of her savings on a laptop that costs $900. How much savings does she have left?
Dana spent 24% of her savings on a laptop that costs $900. How much savings does she have left?
We know that prior to her purchase, $900 was 24% of Dana's Savings. Therefore, Dana's total savings prior to her purchase can be modeled as 
, where 
is Dana's total savings. Solving for 
would give you 
, which indicates that Dana's savings was $3750 prior to her purchase. After her purchase, she will have $2850 left.
We know that prior to her purchase, $900 was 24% of Dana's Savings. Therefore, Dana's total savings prior to her purchase can be modeled as
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% of what number is 900?
% of a number, or, equivalently, 1.5% of a number, is the same as 0.015 multiplied by that number. If we call that number 
, then
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There are 36 blue marbles in a bag. If blue marbles made up 24% of the marbles in the bag, what is the total number of marbles are in the bag?
There are 36 blue marbles in a bag. If blue marbles made up 24% of the marbles in the bag, what is the total number of marbles are in the bag?
If 
is the total number of marbles in the bag, then 
, since 24% of marbles in the bag are blue and there are 36 marbles. Solving for this equation will give you 
, which means there must be a total of 150 marbles in the bag.
If
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12% of the students at a certain high school have perfect attendance. If 27 students have perfect attendance, how many total students does the school contain?
12% of the students at a certain high school have perfect attendance. If 27 students have perfect attendance, how many total students does the school contain?
From the given information here, we know that 12% of the total number equals 27. Mathematically, if we use 
to represent the total that we are looking for, we can write this as
The next step is dividing both sides by 
.
so there are 225 students in the school.
From the given information here, we know that 12% of the total number equals 27. Mathematically, if we use
The next step is dividing both sides by
so there are 225 students in the school.
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is 
of what?
To figure out the value, translate the question into an equation, knowing that "is" means equals, and "of" means multiply:
To solve, turn the percentage into a decimal:
now divide both sides by 0.48
To figure out the value, translate the question into an equation, knowing that "is" means equals, and "of" means multiply:
To solve, turn the percentage into a decimal:
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is 
of what number?
To determine the whole, translate the question into an equation, knowing that "is" means equals and "of" means multiply:
convert the percentage into a decimal:
divide both sides by 1.8
To determine the whole, translate the question into an equation, knowing that "is" means equals and "of" means multiply:
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is 
of what number?
To find the whole from the part given a percentage, we divide our known part by the decimal equivalent of the percentage, which we find by dividing the percentage by one-hundred:
Therefore, 
is 
of 
To find the whole from the part given a percentage, we divide our known part by the decimal equivalent of the percentage, which we find by dividing the percentage by one-hundred:
Therefore,
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If 
of the students in Mrs. Roger's 5th grade class received an "A" on the math test, and the number of students who received an "A" was 12, how many students are there in Mrs. Roger's 5th grade class? Round to the nearest student.
If
If 
of the students in Mrs. Roger's 5th grade class received an "A" on the math test, and the number of students who received an "A" was 
, how many students are there in Mrs. Roger's 5th grade class? Round to the nearest student.
This is question is asking us to find the whole from a percentage and a part. We know that 
students make up 
of the whole class. We need to find the total number of students in the class. The trickiest part of this is the setup.
We can start by thinking of it like so
Meaning that 
of the whole (W) is equal to 
.
Then we use some basic rearranging to divide both sides by 
So there are 
students in the class.
Note, there cannot be 
students, because we must round down. 
is not 
or greater, so we cannot round up to 
.
If
This is question is asking us to find the whole from a percentage and a part. We know that
We can start by thinking of it like so
Meaning that
Then we use some basic rearranging to divide both sides by
So there are
Note, there cannot be
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Oscar must pay 
of his annual income in back taxes. The amount taken from Oscar's monthly salary totals $722.85. How much does Oscar make annually before pay deductions?
Oscar must pay
First of all, it should be understood that since 
of Oscar's annual earnings are taken, than 
of his monthly salary is also taken. By that reasoning, 
is 
of Oscar's monthly salary, which we can then use to determine his annual earnings:
First of all, it should be understood that since
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Charlie paid the monthly rent for his Manhattan penthouse of 
. If the cost of rent accounts for 62% of Charlie's income, how much does he make annually?
Charlie paid the monthly rent for his Manhattan penthouse of
We can determine Charlie's monthly earnings given the amount he spends in rent and the percent of his income that it consumes:
With this value we can now determine Charlie's annual income:
We can determine Charlie's monthly earnings given the amount he spends in rent and the percent of his income that it consumes:
With this value we can now determine Charlie's annual income:
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of the eggs gathered in the hen house were brown and there were 
of them. How many eggs in total were gathered?
Since 
eggs account for 
of the total batch, we can determine the total number of eggs as such:
Since
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For helping run the snack bar Rodney was paid 
of total earnings for the day. If Rodney was paid 
, what was the total earnings for the snack bar?
For helping run the snack bar Rodney was paid
Dividing 
of the total earnings by 
will determine the total amount of money earned:
Dividing
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Todd has paid for 
of the semester's tuition at the University of Alaska. If Todd still owes 
, what is the total cost of the semester's tuition? Round to the nearest dollar.
Todd has paid for
If Todd has already paid 
of his tuition, then he still owes 
of the total cost. 
is 
of the total cost of tuition, which we can use to calculate the full cost:
If Todd has already paid
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30% of what number is 6?
30% of what number is 6?
When we don't know the value of a number, we assign it a variable. In this case,
30% of what number is 6
can be written as
30% of x is 6
Now, we will write 30% as a decimal. We get
0.3 of x is 6
We know when we see "is" that means equals. So,
0.3 of x = 6
We also know when we are finding percentages of numbers, we multiply. So,
Now, we solve for x. We divide both sides by 0.3. We get
Therefore, 30% of 20 is 6.
When we don't know the value of a number, we assign it a variable. In this case,
30% of what number is 6
can be written as
30% of x is 6
Now, we will write 30% as a decimal. We get
0.3 of x is 6
We know when we see "is" that means equals. So,
0.3 of x = 6
We also know when we are finding percentages of numbers, we multiply. So,
Now, we solve for x. We divide both sides by 0.3. We get
Therefore, 30% of 20 is 6.
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You are given an allowance and told by your parents that since times are tough they are cutting your allowance and you will only be getting 
of your normal allowance. Your mother then hands you 
. How much money were you getting before your pay cut?
You are given an allowance and told by your parents that since times are tough they are cutting your allowance and you will only be getting
You are getting 
of the total value you once received, which is 
. This looks like
Or, using the decimal equivalent,
where 
is the total amount we are looking for. You can divide both sides by 
to solve for 
,
You are getting
Or, using the decimal equivalent,
where
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