Algebra 1 : How to find the whole from the part with percentage

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #11 : Whole And Part

 is  of what number?

Possible Answers:

Correct answer:

Explanation:

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 

Example Question #12 : Whole And Part

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.

Possible Answers:

Correct answer:

Explanation:

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 .

Example Question #12 : Whole And Part

 of the eggs gathered in the hen house were brown and there were  of them. How many eggs in total were gathered?

Possible Answers:

Correct answer:

Explanation:

Since  eggs account for  of the total batch, we can determine the total number of eggs as such:

Example Question #13 : Whole And Part

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?

Possible Answers:

Correct answer:

Explanation:

Dividing  of the total earnings by  will determine the total amount of money earned:

Example Question #14 : Whole And Part

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. 

Possible Answers:

Correct answer:

Explanation:

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:

Example Question #15 : Whole And Part

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? 

Possible Answers:

Correct answer:

Explanation:

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:

Example Question #16 : Whole And Part

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?

Possible Answers:

Correct answer:

Explanation:

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:

Example Question #17 : Whole And Part

30% of what number is 6?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #11 : How To Find The Whole From The Part With Percentage

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?

Possible Answers:

Correct answer:

Explanation:

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 ,

Example Question #12 : How To Find The Whole From The Part With Percentage

One percent of a number is two.  What is that number?

Possible Answers:

Correct answer:

Explanation:

One percent is one out of 100 parts.  Write the fraction conversion of the percent.

This value times a number is equal to two.  Write the equation to express this.

To solve for , multiply by 100 on both sides.

Simplify both sides.

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