how to solve word problems with percentage

Percentages in Word Problems

Hi, and welcome to this video lesson on percentages in word problems.

I know word problems are most people’s worst nightmare, but never fear, we’re going to learn how to turn a big, scary, word percentage problem into a 3-step breeze!

Okay, let’s look at our problem:

The bill for dinner is $62.00. The diners decide to leave their server a 20% tip. Determine the total cost of dining at the restaurant, including tip.

Okay, so what is our goal? We always want to understand the goal in a word problem. Our goal here is: “Determine the total cost of dining at the restaurant, including tip.” That means finding the cost of the meal and finding the cost of the tip so we can add them together. We already know the bill for dinner, so we’re halfway home. Let’s solve the rest of this problem in three easy steps.

STEP 1: Change the percentage to a decimal. Remove the % sign from the 20% and drop a period in front of the 20 so we have .20. We are allowed to do this because when we are finding percents, we are really multiplying a decimal number against another number. This is because 20 percent of a number can be written as a ratio of a part per hundred: \(20\% = \frac{20}{100}=.20\)

STEP 2: Multiply the bill by 0.20 to find the amount of the tip: \($62.00(0.20)=$12.40\)

STEP 3: Add the tip and bill to find the total. The total cost of dining will be the sum of the bill for dinner and the tip: \($62.00+$12.40=$74.40\)

The total cost is $74.40.

I hope that helps. Thanks for watching this video lesson, and, until next time, happy studying.

Percent Word Problems

  Lauren went to her favorite taco truck for lunch. Her bill was $24.80, and she wants to leave a 20% tip. Help Lauren determine what her tip should be.

The correct answer is Tip $4.96. In order to calculate Lauren’s tip, we need to determine what 20% of $24.80 is. Let’s convert 20% to a decimal, which would be 0.20. Now we can simply multiply \($24.80×0.20\) in order to determine the tip. \($24.80×0.20=$4.96\)

  Michael wants to mow lawns in order to make some extra money this summer, but he needs to find a lawn mower to use. Michael’s brother tells him that he will loan Michael his lawn mower if he gives him 4% of the money he makes on each lawn. If Michael agrees, and he earns 40 dollars on his first lawn mowed, how much money does he own his brother?

The correct answer is $1.60. In order to calculate 4% of 40, we need to convert 4% to a decimal. 4% is 0.04 as a decimal. Now we can multiply 0.04 and $40 in order to determine what Michael owes his brother. \(0.04×$40=1.6=$1.60\)

  In a study of 250 high school students, 90% of students have taken the driver’s education course. How many students have not taken the course?

15 students

20 students

25 students

30 students

The correct answer is 25 students. 90% of the students have taken the driver’s education course, and there are 250 students total. Let’s start by determining how many students have taken the course. To do this we can multiply \(0.9×250\) which equals 225. This means that 225 students have taken the course. If 225 students have taken the course, and there are 250 students total, we can find the difference between 225 and 250 in order to determine how many students have not taken the course. \(250-225=25\) students have not taken the course.

  Julian scored 90% on his math test. The test had 60 questions. How many questions did he answer correctly?

The correct answer is 54. If Julian answered 90% of the questions correctly, and there were 60 questions total, we can calculate 90% of 60 in order to determine how many questions he answered correctly. Let’s convert 90% to a decimal (0.9), and then multiply this by 60. \(0.9×60=54\) questions answered correctly

  A video game costs $45 before tax. If the sales tax is 5%, what will the total cost of the game be including tax?

The correct answer is $47.25. Let’s first calculate the tax. If the game costs $45 and the tax is 5%, we can multiply \(45×0.05\) in order to determine the tax. \(45×0.05 = 2.25\), which means there will be a $2.25 tax on the purchase. Now let’s add this tax to the price of the game in order to calculate the total cost of the game plus the tax. \($45+$2.25=$47.25\)

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Percentage word problems

Before you take a look at the percentage word problems in this lesson and their solutions, it may help to review the lesson about  formula for percentage or you can use the different techniques that I use here.

Different types of percentage word problems

There are three different types of percentage word problems. We will show how to solve them using proportions. 

• What is 80% of 20? ( example #1 )
• 50 is 25% of what number? ( example #2 )
• 18 is what percent of 24? What percent of 2000 is 3500? ( example #3 and example #4 )

Solving percentage word problems using proportions

You can solve problems involving percents using the proportion you see in the figure above:   ( n% / 100% = Part / Whole )

First, study the figure carefully! Then, we will show how to use the proportion to solve percentage word problems by creating diagrams to visualize relationships.

Example #1: A test has 20 questions. If peter gets 80% correct, how many questions did peter miss?

First, you need to find the number of correct answers by looking for 80% of 20.

When the problem involves looking for the part or the problem says something like, "Find 80% of 20" or "Find 30% of 50," just change the percent to a decimal and multiply.

80% of 20 = (80 / 100) × 20 = 0.80 × 20 = 16

Since the test has 20 questions and he got 16 correct answers, the number of questions Peter missed is 20 − 16 = 4

Recall that 16 is called the percentage. It is the answer you get when you take the percent of a number.

Percentage  =   Part

Example #2: In a school, 25% of the teachers teach basic math. If there are 50 basic math teachers, how many teachers are there in the school?

Once again set the problem up as shown in the figure below. Notice that the question is, " How many teachers are in the school?"

Therefore, the whole is missing this time!

Method #2 I shall help you reason the problem out!

When we say that 25% of the teachers teach basic math, we mean 25% of all teachers in the school equals number of teachers teaching basic math.

Since we don't know how many teachers there are in the school, we replace this with x or a blank. However, we know that the number of teachers teaching basic math is equal to the percentage = part =  50 Putting it all together, we get the following equation: 25% of ____ = 50 or 25% × ____ = 50 or 0.25 × ____ = 50 Thus, the question is 0.25 times what gives me 50? A simple division of 50 by 0.25 will get you the answer 50 / 0.25 = 200 Therefore, we have 200 teachers in the school In fact, 0.25 × 200 = 50

More percentage word problems

Example #3: 24 students in a class took an algebra test. If 18 students passed the test, what percent do not pass?

Solution First, find out how many student did not pass. Number of students who did not pass is 24 − 18 = 6

Then, write down the following equation: x% of 24 = 6 or x% × 24 = 6

To get x%, just divide 6 by 24 6 / 24 = 0.25 = 25 / 100 = 25% Therefore, 25% of students did not pass.

Example #4: A fundraising company would like to raise $2000 for a cause. The fundraiser was so successful that they ended up raising $3500. What percent of their goal did they raise?

Notice that the whole is 2000 since this is the whole money they expect to raise. The part is the amount that the fundraiser ended with and it usually lower than the amount they expect to raise. However, in this particular case, the part ended up being bigger than the whole. Keeping this in mind, here is how to set it up and solve it!

The fundraising company was able to raise 175% of the expected amount.

Example #5:

A department has a total of 22,000 units of stock. 25% of the garments are black and 10% of the garments are size 14.

a) How many black garments are there? 
b) How many size 14 garments are there? 
c) If 10% of the black garments are size 14,how many garments are black and size 14?

Note that the solution we show below for example #5 use a completely different approach or technique. Read it carefully and try to learn it as well!

25% = 25 per 100 = 250 per 1000 For 22,000 just multiply 250 by 22 250    ×    22   =  250 × (10 + 10 + 2)

                       =  2500 + 2500 + 500                        =  5000 + 500                        =  5500

So, there are 5500 black garments.

10% = 10 per 100 = 100 per 1000 For 22,000 just multiply 100 by 22 100 × 22 = 2200 So, 2200 of the garments are size 14.

If 10% or 10 per 100 of the black garments are size 14, then 100 per 1000 of the black garments are size 14.

500 per 5000 are size 14. However, you need to find it for 5500 black garments.

Then, what is 10% of 500? 10% = 10 per 100, so 50 per 500. So 550 of the black garments are size 14.

If you really understand the percentage word problems above, you can solve any other similar percentage word problems. If you still do not understand them, I strongly encourage you to study them again and again until you get it. The end result will be very rewarding!

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Basic "Percent of" Word Problems

Basic Set-Up Markup / Markdown Increase / Decrease

When you learned how to translate simple English statements into mathematical expressions, you learned that "of" can indicate "times". This frequently comes up when using percentages.

Suppose you need to find 16% of 1400 . You would first convert the percentage " 16% " to its decimal form; namely, the number " 0.16 ".

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Percent Word Problems

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Why does the percentage have to be converted to decimal form?

When you are doing actual math, you need to use actual numbers. Percents, being the values with a "percent" sign tacked on, are not technically numbers. This is similar to your grade-point average ( gpa ), versus your grades. You can get an A in a class, but the letter "A" is not a numerical grade which can be averaged. Instead, you convert the "A" to the equivalent "4.0", and use this numerical value for finding your gpa .

When you're doing computations with percentages, remember always to convert the percent expressions to their equivalent decimal forms.

Once you've done this conversion of the percentage to decimal form, you note that "sixteen percent OF fourteen hundred" is telling you to multiply the 0.16 and the 1400 . The numerical result you get is (0.16)(1400) = 224 . This value tells you that 224 is sixteen percent of 1400 .

How do you turn "percent of" word problems into equations to solve?

Percentage problems usually work off of some version of the sentence "(this) is (some percentage) of (that)", which translates to "(this) = (some decimal) × (that)". You will be given two of the values — or at least enough information that you can figure out what two of the values must be — and then you'll need to pick a variable for the value you don't have, write an equation, and solve the equation for that variable.

What is an example of solving a "percent of" word problem?

• What percent of 20 is 30 ?

We have the original number 20 and the comparative number 30 . The unknown in this problem is the rate or percentage. Since the statement is "(thirty) is (some percentage) of (twenty)", then the variable stands for the percentage, and the equation is:

30 = ( x )(20)

30 ÷ 20 = x = 1.5

Since x stands for a percentage, I need to remember to convert this decimal back into a percentage:

Thirty is 150% of 20 .

What is the difference between "percent" and "percentage"?

"Percent" means "out of a hundred", its expression contains a specific number, and the "percent" sign can be used interchangeably with the word (such as " 24% " and "twenty-four percent"); "percentage" is used in less specific ways, to refer to some amount of some total (such as "a large percentage of the population"). ( Source )

In real life, though, including in math classes, we tend to be fairly sloppy in using these terms. So there's probably no need for you to worry overmuch about this technicallity.

• What is 35% of 80 ?

Here we have the rate (35%) and the original number (80) ; the unknown is the comparative number which constitutes 35% of 80 . Since the exercise statement is "(some number) is (thirty-five percent) of (eighty)", then the variable stands for a number and the equation is:

x = (0.35)(80)

Twenty-eight is 35% of 80 .

• 45% of what is 9 ?

Here we have the rate (45%) and the comparative number (9) ; the unknown is the original number that 9 is 45% of. The statement is "(nine) is (forty-five percent) of (some number)", so the variable stands for a number, and the equation is:

9 = (0.45)( x )

9 ÷ 0.45 = x = 20

Nine is 45% of 20 .

The format displayed above, "(this number) is (some percent) of (that number)", always holds true for percents. In any given problem, you plug your known values into this equation, and then you solve for whatever is left.

• Suppose you bought something that was priced at $6.95 , and the total bill was $7.61 . What is the sales tax rate in this city? (Round answer to one decimal place.)

The sales tax is a certain percentage of the price, so I first have to figure what the actual numerical amount of the tax was. The tax was:

7.61 – 6.95 = 0.66

Then (the sales tax) is (some percentage) of (the price), or, in mathematical terms:

0.66 = ( x )(6.95)

Solving for x , I get:

0.66 ÷ 6.95 = x      = 0.094964028... = 9.4964028...%

The sales tax rate is 9.5% .

In the above example, I first had to figure out what the actual tax was, before I could then find the answer to the exercise. Many percentage problems are really "two-part-ers" like this: they involve some kind of increase or decrease relative to some original value.

Note : Always figure the percentage of change of increase or decrease relative to the original value.

• Suppose a certain item used to sell for seventy-five cents a pound, you see that it's been marked up to eighty-one cents a pound. What is the percent increase?

First, I have to find the absolute (that is, the actual numerical value of the) increase:

81 – 75 = 6

The price has gone up six cents. Now I can find the percentage increase over the original price.

Note this language, "increase/decrease over the original", and use it to your advantage: it will remind you to put the increase or decrease over the original value, and then divide.

This percentage increase is the relative change:

6 / 75 = 0.08

...or an 8% increase in price per pound.

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How to Solve Word Problems Involving the Percentage of a Number?

In this complete step-by-step guide, you will learn how to solve different types of word problems involving the Percentage of a Number.

Percentages are a common concept in mathematics, and they often appear in word problems. Solving word problems involving percentages can be challenging, but it’s a valuable skill to have.

A step-by-step guide to word problems involving the percentage of a number

Since percentages have no dimensions, it is known as dimensionless numbers. The percentage problems may have \(3\) quantities: the percent, the base, and the amount. The percent comes with the percent symbol \((\%)\) or the word “percent.” The base is the total amount. The amount is part of the whole.

Here is a step-by-step guide on how to solve word problems involving percentages:

• Read the problem carefully and identify the information given. This may include the percentage, the whole, and the part. Make sure you understand what is being asked in the problem.
• Identify the keywords or phrases that indicate a percentage is involved. Words such as “percent,” “percentage,” “out of \(100\),” or “per \(100\)” are clues that a percentage is involved.
• Write an equation to represent the information given in the problem.
• Use math operations to solve for the unknown value.
• Check your answer by plugging it back into the original equation and seeing if it is true.

Word Problems Involving the Percentage of a Number – Example 1

The cinema has \(230\) seats. \(161\) seats were sold for the animated movie. What percent of seats are sold?

Solution : 161 is a part of the number \(230\). Let \(x\) represent the percent to find a percent of \(161\) out of \(230\). Write a proportion for \(x\) and solve. \(\frac{161}{230}=\frac{x}{100}→161×100=230x→16100=230x→16100÷230=x→70=x\)

Word Problems Involving the Percentage of a Number– Example 2

There are \(30\) students in a class and 6 of them are girls. What percent are girls? Solution : \(6\) is a part of the number \(30\). Let \(x\) represent the percent to find a percent of \(6\) out of \(30\). Write a proportion for \(x\) and solve. \(\frac{6}{30}=\frac{x}{100}→6×100=30x→600=30x→600÷30=x→20=x\)

by: Effortless Math Team about 1 year ago (category: Articles )

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Tricks to Solving Percentage Word Problems

How to Convert Percent to Decimal

Word problems test both your math skills and your reading comprehension skills. In order to answer them correctly, you'll need to examine the questions carefully. Always make sure you know what is being asked, what operations are necessary and what units, if any, you need to include in your answer.

Eliminate Extraneous Data

Sometimes, word problems include extraneous data that is not necessary to solve the problem. For example:

Kim won 80 percent of her games in June and 90 percent of her games in July. If she won 4 games in June and played 10 games in July, how many games did Kim win in July?

The simplest way to eliminate extraneous data is to identify the question; in this case, "How many games did Kim win in July?" In the example above, any information that doesn't deal with the month of July is unnecessary to answer the question. You are left with 90 percent of 10 games, allowing you to do a simple calculation:

0.9*10=9 games

Calculate Additional Data

Read the question portion twice to make sure you know what data you need to answer the question:

On a test with 80 questions, Abel got 4 answers wrong. What percentage of questions did he get right?

The word problem only gives you two numbers, so it would be easy to assume that the questions involves those two numbers. However, in this case, the question requires that you calculate another answer first: the number of questions Abel got right. You'll need to subtract 4 from 80, then calculate the percentage of the difference:

80-4=78, and 78/80*100=97.5 percent

Rephrase Difficult Problems

Remember that you can often rearrange problems to make them simpler. This is especially useful if you don't have a calculator available:

Gina needs to score at least 92 percent on her final exam to get an A for the semester. If there are 200 questions on the exam, how many questions does Gina need to get right in order to earn an A?

The standard approach would be to multiply 200 by 0.92: 200*.92=184. While this is a simple process, you can make the process even simpler. Instead of finding 92 percent of 200, find 200 percent of 92 by doubling it:

This method is particularly useful when you are dealing with numbers with known ratios. If, for example, the word problem asked you to find 77 percent of 50, you could simply find 50 percent of 77:

50*.77=38.5, or 77/2=38.5

Account for Units

Convert your answers into appropriate units:

Cassie works from 7 a.m. to 4 p.m. each weekday. If Cassie worked 82 percent of her shift on Wednesday and worked 100 percent of her other shifts, what percent of the week did she miss? How much time did she work in total?

First, calculate how many hours Cassie works per day, taking noon into account, then per week:

4+(12-7)=9 9*5=45

Next, calculate 82 percent of 9 hours:

0.82*9=7.38

Subtract the product from 9 for the total hours missed:

9-7.38=1.62

Calculate what percentage of the week she missed:

1.62/45*100=3.6 percent

The second question asks for an amount of time, which means you'll need to convert the decimal into time increments. Add the product to the other four work days:

7.38+(9*4)=43.38

Convert the decimal into minutes:

0.38*60=22.8

Convert the remaining decimal into seconds:

So Cassie missed 3.6 percent of her week, and worked 43 hours, 22 minutes and 48 seconds total.

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• Central New Mexico Communicty College: Percent Word Problems
• Basic Mathematics: Percentage Word Problems

About the Author

Since 2003, Momi Awana's writing has been featured in "The Hawaii Independent," "Tradewinds" and "Eternal Portraits." She served as a communications specialist at the Hawaii State Legislature and currently teaches writing classes at her library. Awana holds a Master of Arts in English from University of Hawaii, Mānoa.

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Percentage Increase and Decrease Word Problems

• To find 10%, divide a number by 10.
• The original mass of chocolate is 200 grams.
• 200 ÷ 10 = 10 and so 10% of 200 grams in 20 grams.
• To increase an amount by 10%, add 10% to the original amount.
• 200 + 20 = 220. Therefore the new mass is 220 grams

• To find 40%, first find 10% and then multiply it by 4.
• 10% is found by dividing the number by 10. £50 ÷ 10 = £5 and so, 10% is £5.
• We multiply 10% by 4 to get 40%. £5 × 4 = £20 and so, 40% is £20.
• In a sale, the price is decreased.
• To decrease by a percentage, subtract the percentage from the original number.
• £50 – £20 = £30 and so, the new price is £30.

• Percentages of Amounts

Percentage Change Word Problems

How to work out percentage change.

• Work out the percentage by dividing the original number by 100 and multiplying by the percentage.
• For a percentage increase, add this percentage to the original number.
• For a percentage decrease, subtract this percentage from the original number.

• To find 1%, divide by 100.
• To find 5%, divide by 20.
• To find 10%, divide by 10.
• To find 20%, divide by 5.
• To find 25%, divide by 4.
• To find 50%, divide by 2.

Percentage Increase Word Problems

Percentage Decrease Word Problems

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Percentage Word Problems

Welcome to our Basic Percentage Word Problems. In this area, we have a selection of basic percentage problem worksheets designed for 6th grade students who are just starting to learn about percentages to help them to solve a range of simple percentage problems.

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Percentage Learning

Percentages are another area that children can find quite difficult. There are several key areas within percentages which need to be mastered in order.

Our selection of percentage worksheets will help you to find percentages of numbers and amounts, as well as working out percentage increases and decreases and converting percentages to fractions or decimals.

Key percentage facts:

• 50% = 0.5 = ½
• 25% = 0.25 = ¼
• 75% = 0.75 = ¾
• 10% = 0.1 = 1 ⁄ 10
• 1% = 0.01 = 1 ⁄ 100

How to work out Percentages of a number

This page will help you learn to find the percentage of a given number.

There is also a percentage calculator on the page to support you work through practice questions.

• Percentage Of Calculator

This is the calculator to use if you want to find a percentage of a number.

Simple choose your number and the percentage and the calculator will do the rest.

Basic Percentage Word Problems

Here you will find a selection of worksheets on percentages designed to help your child practise how to apply their knowledge to solve a range of percentage problems..

The sheets are graded so that the easier ones are at the top.

The sheets have been split up into sections as follows:

• spot the percentage problems where the aim is to use the given facts to find the missing percentage;
• solving percentage of number problems, where the aim is to work out the percentage of a number.

Each of the sheets on this page has also been split into 3 different worksheets:

• Sheet A which is set at an easier level;
• Sheet B which is set at a medium level;
• Sheet C which is set at a more advanced level for high attainers.

Spot the Percentages Problems

• Spot the Percentage 1A
• PDF version
• Spot the Percentage 1B
• Spot the Percentage 1C
• Spot the Percentage 2A
• Spot the Percentage 2B
• Spot the Percentage 2C

Percentage of Number Word Problems

• Percentage of Number Problems 1A
• Percentage of Number Problems 1B
• Percentage of Number Problems 1C
• Percentage of Number Problems 2A
• Percentage of Number Problems 2B
• Percentage of Number Problems 2C
• Percentage of Number Problems 3A
• Percentage of Number Problems 3B
• Percentage of Number Problems 3C

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

6th Grade Percentage Word Problems

The sheets in this area are at a harder level than those on this page.

The problems involve finding the percentage of numbers and amounts, as well as finding the amounts when the percentage is given.

• 6th Grade Percent Word Problems
• Percentage Increase and Decrease Worksheets

We have created a range of worksheets based around percentage increases and decreases.

Our worksheets include:

• finding percentage change between two numbers;
• finding a given percentage increase from an amount;
• finding a given percentage decrease from an amount.

Percentage of Money Amounts

Often when we are studying percentages, we look at them in the context of money.

The sheets on this page are all about finding percentages of different amounts of money.

• Money Percentage Worksheets

Percentage of Number Worksheets

If you would like some practice finding the percentage of a range of numbers, then try our Percentage Worksheets page.

You will find a range of worksheets starting with finding simple percentages such as 1%, 10% and 50% to finding much trickier ones.

• Percentage of Numbers Worksheets

Converting Percentages to Fractions

To convert a fraction to a percentage follows on simply from converting a fraction to a decimal.

Simply divide the numerator by the denominator to give you the decimal form. Then multiply the result by 100 to change the decimal into a percentage.

The printable learning fraction page below contains more support, examples and practice converting fractions to decimals.

• Converting Fractions to Percentages

• Convert Percent to Fraction

Online Percentage Practice Zone

Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers.

You can choose your level of difficulty and test yourself with immediate feedback!

• Online Percentage Practice
• Ratio Part to Part Worksheets

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• Percentage Word Problems

Introduction

Percentage is basically the ratio of the value of a particular quantity to its total value multiplied by 100. It is generally a way of expressing something as per 100. Further, in this article we will look at various scenarios for which we will find the percentage and learn the steps to solve word problems based on percentage.

What is the Percentage?

A percentage is something expressed part per hundred. It is generally a ratio which is given in terms of a fraction of 100. The word percent is taken from the Latin term per centrum which means “by the hundred” . It is denoted by the symbol “\[\% \]”.

What is Percentage

How to Calculate the Percentage?

Percentage is generally calculated by expressing the value whose percentage is to be calculated and the total value as a ratio which is multiplied by 100. The formula for calculating percentage is as follows :

Percentage \[ = \frac{{value}}{{Total\,Value}} \times 100\]

If in case, percentage of a number is to be calculated i.e. if % is given and the value of the quantity whose percentage is given with respect to the total is to be found we use -

For instance,\[{\rm{x\% }}\] of 450 \[ = \]Y and we wish to calculate the value of Y, we can do so by

\[{\rm{Y}} = \frac{{\rm{X}}}{{100}} \times 450\]

E.g. 20% of 800

So, \[\frac{{20}}{{100}} \times 800 = 20 \times 8 = 160\]

Question and Answer based on Percentage

This section contains basic problems based on the concept of percentage which can be solved very easily.

Raju scored 81 out of 90 in mathematics. Convert his marks into percentages.

Ans. Percentage \[ = \] Value \[/\]Total Value \[ \times \]100 \[ = \frac{{81}}{{90}} \times 100 = 9 \times 10 = 90\% \]

In a class of 300 students, there are 75 girls. Calculate the percentage of boys in the class.

Ans. Number of boys \[ = 300 - 75 = 225\]

Percentage of boys \[ = \frac{{225}}{{300}} \times 100 = 75\% \]

Prince spent 75 \[\% \] of the money he had to buy groceries. If he had 4000$ with him initially, what amount did he spend ?

Ans. Amount Spend \[ = \frac{{75}}{{100}} \times 4000 = 3000\]$

Compute 65% of 680

Ans. 65% of 680 \[ = \frac{{65}}{{100}} \times 680 = 442\]

Word Problems based on Percentage

The word problem based on percentage will have some scenarios in which we have to understand the requirements in the given problems and accordingly apply the formula for percentage and find the value of the quantity asked to be found.

1.If a brass article contains 72% of copper. What amount of brass will be required to get 360g of copper?

Ans : Let the quantity of brass required be x g.

Therefore, 72% of x = 360g

\[72\% \, \times \,x = 360g\]

\[0.72 \times x = 360g\]

Therefore, \[x = \frac{{360}}{{0.72}} = 500g\]

So, 500 g of brass is required to get 360g of copper.

2.Karishma appeared for a quiz in which she got 25 answers correct and 15 answers incorrect. What is the percentage of questions that she appeared correctly ?

Ans : Here, in this case 25 answers were correct and 15 were incorrect.

Therefore, total questions \[ = 25 + 15 = 40\]

So, Percentage of correct questions \[ = \frac{{25}}{{40}} \times 100 = 62.5\% \]

Therefore, 62.5\[\% \] of the questions were answered correctly by Karishma.

Solved Examples :

1. What is 30\[\% \] of 450?

Solution : 30 % of 450 \[ = \frac{{30}}{{100}} \times 450 = 0.3 \times 450 = 135\]

Therefore, 30% of 450 is 135.

2. The cost price of a bag is 1500 and the selling price of the same bag is 2100. At what profit is the article sold? What is the profit percentage?

Solution : As , Profit = Selling price - Cost price

Therefore, Profit earned on selling the bag \[ = 2100 - 1500 = 600\]

So, Profit Percentage \[ = \frac{{600}}{{1500}} \times 100 = 40\% \]

The seller earned 40\[\% \] profit on selling the bag.

3. Arun sells an object to Benny at a profit of 15%, Benny sells that object to Chandan for ₹1012 and makes a profit of 10%. At what cost did Arun purchase the object?

Solution: Let the actual cost price at which Arun bought the object be x

When Arun sells the object to Benny

Profit % = 15%

∴ selling price of object \[= \frac{{100 + 15}}{{100}} \times x = 1.15x\]

Now, this cost price of the object for Benny

When Benny sells the object to Chandan

Selling Price = ₹1012

Profit % = 10%

∴ Selling price = \[ = \frac{{100 + 10}}{{100}} \times 1.15x\]

\[ \Rightarrow 1012 = \frac{{100 + 10}}{{100}} \times 1.15x\]

\[ \Rightarrow x = \frac{{1012 \times 1000}}{{11 \times 115}}\]

Therefore, the price at which Arun bought the object is ₹800.

4. In an inter school aptitude test, 200 students appeared. Out of these students; 20 % got A grade, 50 % got B grade and the remaining got C grade. Assuming that no student got a D grade; find the number of students who got a C grade .

Solution : The number of students with A grade \[ = \] 20 \[\% \] of 200

\[ = \frac{{20}}{{100}} \times 200 = \frac{{4000}}{{100}}\]

And, the number of students with B grade \[ = \] 50 \[\% \] of 200

\[ = \frac{{50}}{{100}} \times 200\]

\[ = \frac{{10000}}{{100}} = 100\]

Therefore, the number of students who got C grade \[ = 200 - [40 + 100]\]

\[ = 200 - 140 = 60\]

So, 60 students scored C grade.

Conclusion:

Thus, we can say that percentage is a fraction of something expressed as part of 100. So, after understanding the method of calculating percentage and applying it according to the scenario we can easily solve the word problems based on percentage.

FAQs on Percentage Word Problems

1. Can the percentage be negative?

No, percentage can never be negative.

2. Is 0% of something valid ?

Yes, it is valid. For instance, if an alloy contains 0% of a certain element it simply means that the element is not present in that alloy.

Example: \[1250 \times 0\%  = 0\]

3. Can percentage be represented in decimals?

Yes, percentage can be represented in decimals. For example, 25% of something means \[\frac{{25}}{{100}} = 0.25\]\[\frac{{25}}{{100}} = 0.25\]

4. Can percentages be added?

Yes, percentages can be added if they are taken considering the same total value

Example: 5 % and 10% is 5 + 10 = 15%.

5. Can percentage be rounded off?

Yes, percentages can be rounded off to the nearest next natural number only if fine accuracy in decimals is not required in that scenario.

Example: 7.526% round off is 7.5%

Ratio and Percent Word Problems

Ratio word problems, using table with multiplication.

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Using Tape Diagram

Using Graphs

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How do you solve word problems in math?

Master word problems with eight simple steps from a math tutor!

Author Amber Watkins

Published April 2024

• Key takeaways
• Students who struggle with reading, tend to struggle with understanding and solving word problems. So the best way to solve word problems in math is to become a better reader!
• Mastery of word problems relies on your child’s knowledge of keywords for word problems in math and knowing what to do with them.
• There are 8 simple steps each child can use to solve word problems- let’s go over these together.

Table of contents

• How to solve word problems

Lesson credits

As a tutor who has seen countless math worksheets in almost every grade – I’ll tell you this: every child is going to encounter word problems in math. The key to mastery lies in how you solve them! So then, how do you solve word problems in math?

In this guide, I’ll share eight steps to solving word problems in math.

How to solve word problems in math in 8 steps

Step 1: read the word problem aloud.

For a child to understand a word problem, it needs to be read with accuracy and fluency! That is why, when I tutor children with word problems, I always emphasize the importance of reading properly.

Mastering step 1 looks like this:

• Allow your child to read the word problem aloud to you. 
• Don’t let your child skip over or mispronounce any words. 
• If necessary, model how to read the word problem, then allow your child to read it again. Only after the word problem is read accurately, should you move on to step 2.

Step 2: Highlight the keywords in the word problem

The keywords for word problems in math indicate what math action should be taken. Teach your child to highlight or underline the keywords in every word problem. 

Here are some of the most common keywords in math word problems: 

• Subtraction words – less than, minus, take away
• Addition words – more than, altogether, plus, perimeter
• Multiplication words – Each, per person, per item, times, area 
• Division words – divided by, into
• Total words – in all, total, altogether

Let’s practice. Read the following word problem with your child and help them highlight or underline the main keyword, then decide which math action should be taken.

Michael has ten baseball cards. James has four baseball cards less than Michael. How many total baseball cards does James have? 

The words “less than” are the keywords and they tell us to use subtraction .

Step 3: Make math symbols above keywords to decode the word problem

As I help students with word problems, I write math symbols and numbers above the keywords. This helps them to understand what the word problem is asking.

Let’s practice. Observe what I write over the keywords in the following word problem and think about how you would create a math sentence using them:

Step 4: Create a math sentence to represent the word problem

Using the previous example, let’s write a math sentence. Looking at the math symbols and numbers written above the word problem, our math sentence should be: 10 – 5 = 5 ! 

Each time you practice a word problem with your child, highlight keywords and write the math symbols above them. Then have your child create a math sentence to solve. 

Step 5: Draw a picture to help illustrate the word problem

Pictures can be very helpful for problems that are more difficult to understand. They also are extremely helpful when the word problem involves calculating time , comparing fractions , or measurements . 

Step 6: Always show your work

Help your child get into the habit of always showing their work. As a tutor, I’ve found many reasons why having students show their work is helpful:

• By showing their work, they are writing the math steps repeatedly, which aids in memory
• If they make any mistakes they can track where they happened
• Their teacher can assess how much they understand by reviewing their work
• They can participate in class discussions about their work

Step 7: When solving word problems, make sure there is always a word in your answer!

If the word problem asks: How many peaches did Lisa buy? Your child’s answer should be: Lisa bought 10 peaches .

If the word problem asks: How far did Kyle run? Your child’s answer should be: Kyle ran 20 miles .

So how do you solve a word problem in math?

Together we reviewed the eight simple steps to solve word problems. These steps included identifying keywords for word problems in math, drawing pictures, and learning to explain our answers. 

Is your child ready to put these new skills to the test? Check out the best math app for some fun math word problem practice.

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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Solar Eclipse Math Word Problems, Solar Eclipse 2024 Math Activities Printables.

Description

This engaging collection of math word problems is designed to challenge students' problem-solving abilities while immersing them in real-life scenarios related to solar eclipses.

Aligned with grade-level math standards, this product features 10 thoughtfully crafted word problems covering a range of mathematical operations, including addition, subtraction, multiplication, division, length, time, and more. Each problem incorporates elements of solar eclipses, making math learning both relevant and exciting for students.

With clear step-by-step solutions provided for each problem, teachers can easily guide students through the problem-solving process, fostering a deeper understanding of mathematical concepts in the context of real-world phenomena.

• Engages students in real-life scenarios related to solar eclipses.
• Improves problem-solving skills and critical thinking abilities in a meaningful context.
• Helps students practice various math operations while learning about astronomy.
• Step-by-step solutions provided for better understanding and confidence building.

Instructions :

• This set of math word problems related to solar eclipses can be implemented by printing out the worksheets and distributing them to students for individual or group work.
• Facilitate discussions around the solutions to reinforce key math concepts and techniques.
• Use the completed worksheets as formative assessments to gauge student understanding.

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• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
• What is an age problem?
• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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How Tesla Planted the Seeds for Its Own Potential Downfall

Elon musk’s factory in china saved his company and made him ultrarich. now, it may backfire..

Hosted by Katrin Bennhold

Featuring Mara Hvistendahl

Produced by Rikki Novetsky and Mooj Zadie

With Rachelle Bonja

Edited by Lisa Chow and Alexandra Leigh Young

Original music by Marion Lozano ,  Diane Wong ,  Elisheba Ittoop and Sophia Lanman

Engineered by Chris Wood

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

When Elon Musk set up Tesla’s factory in China, he made a bet that brought him cheap parts and capable workers — a bet that made him ultrarich and saved his company.

Mara Hvistendahl, an investigative reporter for The Times, explains why, now, that lifeline may have given China the tools to beat Tesla at its own game.

On today’s episode

Mara Hvistendahl , an investigative reporter for The New York Times.

Background reading

A pivot to China saved Elon Musk. It also bound him to Beijing .

Mr. Musk helped create the Chinese electric vehicle industry. But he is now facing challenges there as well as scrutiny in the West over his reliance on China.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

Fact-checking by Susan Lee .

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Katrin Bennhold is the Berlin bureau chief. A former Nieman fellow at Harvard University, she previously reported from London and Paris, covering a range of topics from the rise of populism to gender. More about Katrin Bennhold

Mara Hvistendahl is an investigative reporter for The Times focused on Asia. More about Mara Hvistendahl

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