solving word problems using percentages

Percent Word Problems

In these lessons we look at some examples of percent word problems. The videos will illustrate how to use the block diagrams (Singapore Math) method to solve word problems.

Related Pages More Math Word Problems Algebra Word Problems More Singapore Math Word Problems

How to solve percent problems with bar models? Examples:

• Marilyn saves 30% of the money she earns each month. She earns $1350 each month. How much does she save?
• At the Natural History Museum, 40% of the visitors are children. There are 36 children at the museum. How many visitors altogether are at the museum?
• Bill bought cards to celebrate Pi day. He sent 60% of his cards to his friends. He sent 42 cards to his friends. How many cards did he buy altogether?
• Bruce cooked 80% of the pancakes at the pancake breakfast last weekend. They made 1120 pancakes. How many pancakes did Bruce cook?

Sales Tax and Discount An example of finding total price with sales tax and an example of finding cost after discount.

• Alejandro bought a TV for $900 and paid a sales tax of 8%. How much did he pay for the TV?
• Alice saved for a new bike. The bike was on sale for a discount of 35%. The original cost of the bike was $270. How much did she pay for the bike?

Percent Word Problems Example: There are 600 children on a field. 30% of them were boys. After 5 teams of boys join the children on the field, the percentage of children who were boys increased to 40%. How many boys were there in the 5 teams altogether?

Problem Solving - Choosing a strategy to solve percent word problems An explanation of how to solve multi-step percentage problems using bar models or choosing an operation. Example: The $59.99 dress is on sale for 15% off. How much is the price of the dress?

How to solve percent problems using a tape diagram or bar diagram? Example: An investor offers $200,000 for a 20% stake in a new company. What amount does the investor believe the toatl value of the business is worth at this time? How to use a tape diagram or bar diagram to find the answer?

• First draw a bar that represents the company’s whole value.
• Divide into 5 equal parts because 100%/20% = 5.
• Label one side with the percentages.
• Label the other side $200,000 across from 20% because that was given.
• Finish labeling the money side.
• Find solution.

Solve Percent Problems Using a Tape Diagram (Bar Diagram) Example: a) If $300 is increased by 25% what is the new amount? b) What is 19% of 120? c) Joe went to an athletic store to purchase new running shoes. To his surprise, the store was having a 20% off athletic shoes sale. He purchased a new pair of shoes that were regularly priced $60. How much did Joe pay for his shoes?

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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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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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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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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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25 Percentage Word Problems For Year 5 To Year 8 With Tips On Supporting Pupils’ Progress

Emma Johnson

Percentage word problems and the concept of calculating percentages first appears in Upper Key Stage 2. As pupils progress through school from KS2 to KS3, the skills they need to solve percentage word problems develop.

It is important to expose students to percentage word problems alongside any fluency work on percentages, to help them understand how percentages are used in real-life. To help you with this, we have put together a collection of 25 percentage word problems which can be used by pupils from Year 5 to Year 8. Don’t miss our downloadable word problems worksheet to develop these skills further!

How pupils develop the necessary skills to solve percentage word problems

Percentage word problems in the national curriculum.

• Why are word problems important for children’s understanding of percentage 

How to teach solving percentage word problems in KS2 and early KS3

Percentage word problems for year 5, percentage word problems for year 6, percentage word problems for key stage 3, more word problems resources, percentage word problems faqs.

All Kinds of Word Problems Four Operations

Download this free, printable pack of word problems covering all four operations; a great way to build students' problem solving skills.

Initially, pupils are introduced to the per cent symbol (%) in Year 5. At this stage they are expected to understand that percent relates to ‘number of parts per hundred’ and should be able to solve problems requiring knowing percentage and decimal form equivalents of simple fractions.

As pupils progress into Year 6, they should be able to recall and use equivalences between simple fractions, mixed numbers, decimals and percentages. They also need to be able to solve word problems involving percentages of amounts and percentage increase and decrease.

Moving into Key Stage 3, pupils continue to build on the percentage work from primary, to solve percent problems, interpreting percentages and percentage change; expressing one quantity as a percentage of another; comparing two quantities using percentages and working with percentages greater than 100%.

Concrete resources (such as percentages cubes) and visual images (such as bar models) are important during the early stages of learning and understanding percentages. Word problems for year 3 and word problems for year 4 will often include visual aids. Upper Key Stage 2 teachers and pupils often have the mistaken belief that concrete resources are only for children who are struggling; however, with a new topic, such as percentages, it is important all children are initially introduced to the topic through the use of visual and concrete aids.

Children are first introduced to percentage problems in Year 5. The National Curriculum expectations for percentages are that children will be able to:

Percentage in Year 5

• Recognise the percent symbol (5)  and understand that per cent relates to ‘number of parts per hundred’.
• Write percentages as a fraction with a denominator 100, and in its decimal form.
• Solve problems which require knowing percentage and decimal equivalents of \frac{1}{2},\frac{1}{4},\frac{1}{5},\frac{2}{5},\frac{4}{5} , and fractions with a denominator of a multiple of 10 or 25.

Percentage in Year 6

• Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.
• Solve problems involving the calculation of percentages (for example, measures and such as 15% of 360) and use percentages for comparison.

Percentage in Key Stage 3

• Define percentage as ‘number of parts per hundred’
• Interpret percentages and percentage changes as a fraction or a decimal. Interpret these multiplicatively.
• Express one quantity as a percentage of another.
• Compare two quantities using percentages.
• Work with percentages greater than 100%.
• Interpret fractions and percentages as operators.

Percentage word problems will often include other skills, such as fraction word problems , multiplication word problems , addition word problems , subtraction word problems and division word problems .

Why are word problems important for children’s understanding of percentage 

Percentage word problems help children to develop their understanding of percentages and the different ways percentages are used in everyday life. Taken out of context, percentages can be quite an abstract concept, which some children can find quite difficult to understand. 

Real-life problems involving percentages enable students to see how they will make use of this key skill outside the classroom.

As with all word problems, students need to learn the skills required to solve percentage word problems. It’s important that children make sure they have read the questions carefully and thought about exactly what is being asked and whether they have fully understood this. They then need to identify what they will need to do to solve the problem and whether there are any concrete resources or pictorial representations which they can use to help them. Even pupils in Key Stage 3 can benefit from drawing a quick picture, to understand what a word problem is asking.

Third Space Learning’s online, one-to-one tutoring programmes work to build students’ maths fluency and reasoning skills. Personalised to the needs of each individual student, our programmes fill gaps and build students’ confidence in maths.

Percent word problem example :

A box of cupcakes sold by a bakery cost £3.40.

Due to the increased costs involved with running a bakery, the owner has decided to increase the price of everything sold by 20%.

How much will a box of cupcakes cost once the price has been increased?

How to solve step-by-step:

What do you already know?

–        We know that the original price of a box of cupcakes is £3.40.

–        If the price of the box is being increased by 20%, we need to work out how much 20% of £3.40 is.

–        To do this, we need to work out how much 10% of £3.40 is. We therefore need to divide £3.40 by 10 = £0.34

–        To calculate what 20% is, we need to multiply the £0.34 by 2 = £0.68

–        Finally, we need to add the 20% (£0.68) onto the original price.

–        £3.40 + £0.68 = £4.08

How can this be represented pictorially?

• We can draw a bar model to represent what 10% of £3.40 equals.
• Once we know what 10% of £3.40 is (34p), we can double it to calculate 20% of £3.40 (68p).
• We can then add this on to the original price of £3.40.
• £3.40 + 68p = £4.08.

To solve word problems for year 5 , children need to be able to convert fractions to percentages and calculate fractions of an amount.

Gemma saves \frac{1}{2} of her pocket money every week.

She receives £5 per week and is saving to buy a game costing £25.

• What percentage does she save each week?
• How long will it take her to save for the game?
• She saves 50% of her pocket money each week

Gemma saves £2.50 per week.

£2.50 x 10 = £25

Sam gives \frac{4}{10} of his sweets to Ahmed.

What percentage of the sweets does he keep for himself?

Answer : 60%

  \frac{4}{10} =  \frac{40}{100} = 40%

100 – 40 = 60%

A school football team has 11 players and 5 substitutes.

  \frac{3}{4} of the players are boys, the rest are girls.

What percentage are girls?

Answer: 25%

\frac{3}{4} of 16 are boys

  \frac{1}{4} are girls

  \frac{1}{4} = 25%

Children in Year 5 voted on their favourite food.

35% of children voted for pizza.

60 children took part in the survey.

How many voted for pizza?

Answer : 21 children 

10% of 60: 60 ÷ 10 = 6

5% of 60: Half of 10% (6) = 3

30%: 6 x 3 = 18

35% = 18 + 3 = 21

Ben was given a maths worksheet to complete for his homework.

He got  \frac{6}{10} of the maths problems correct

If there were 20 questions on the paper:

• How many questions did he get right?
• What percentage did he score?

  \frac{1}{10} of 20  = 2

  \frac{6}{10} of 20  = 12

• 60% correct

  \frac{12}{20} =  \frac{60}{100} .

An ice cream seller has been researching the most popular ice creams.

He knows the percentage of each flavour of ice cream sold, but wants to work out how many of each flavour were sold.

80 ice creams were sold in total.

40% vanilla

25% strawberry

20% cookie dough

15% mint choc chip

How many of each ice cream flavour were sold?

20 strawberry

16 cookie dough

12 mint choc chip

10% of 80 = 8 ice creams

5% of 80 = 4 ice creams

Vanilla: 4 x 8 = 32

Strawberry: 2 x 8 = 16. 16 + 4 = 20

Cookie dough: 2 x 8 = 16

Mint choc chip: 8 + 4 = 12

Pupils in Year 5 held a vote on where to go for their next school trip.

The vote was between the zoo and the aquarium.

90 children voted. 

40% voted for the zoo

How many pupils voted for the aquarium?

Answer : 54 children

60% voted for the aquarium

10% of 90 = 9 children

60% = 6 x 9 = 54 children

The price of burgers being sold by a burger van have increased by 25%

If the original price was £2 per burger. How much are the burgers now?

Answer : £2.50

25% of £2 = £2 ÷ 4 = 50p

£2 + 50p = £2.50

Word problems for year 6 involve solving problems involving equivalence between fractions, decimals and percentages; calculation of percentages and using percentages for comparison. Year 6 students will also tackle multi-step problems .

A rugby game lasts for 80 minutes.

A player is on the pitch for 85% of the game.

How long is he on the pitch for?

Answer : 68 minutes

10% of 80  = 8 minutes

5%  = Half of 8 minutes = 4 minutes

80% = 8 x 8 = 64 minutes

64 + 4 = 68 minutes

There are 480 pupils in a primary school.

15% in foundation

25% in Key Stage 1

How many pupils are in Key Stage 2?

Answer : 288 pupils

In foundation there are 15% + 25% (40% of the pupils)

Therefore, 60% of pupils are in KS2

10% of 480 = 48 pupils

60% = 6 x 48 = 288 pupils

A pizza restaurant decided to add a 15% increase to the cost of all their pizzas.

The cost of a meat feast pizza before the increase was £12.60

What is the new price of the pizza?

Answer : £14.49

10% of £12.60 = £1.26

5% = Half of £1.26 = £0.63

15% = £1.26 + £0.63 = £1.89

New price: £12.60 + £1.89 = £14.49

Oliver was shopping for a new pair of jeans.

The jeans were 15% off  in the sale, but the new sale price sticker had fallen off.

The original price of the jeans was £35.

How much did they cost in the sale?

Answer : £29.75

10% of £35 = £3.50

5% = Half of £3.50 = £1.75

35% = £3.50 + £1.75 = £5.25

New price: £35 – £5.25 = £29.75

200g of sugar is needed for a chocolate brownies recipe.

A 1kg bag of sugar is used.

25% of the remaining sugar is used to bake a cake too.

How much sugar was used to bake the cake?

Answer : 200g sugar

 200g sugar used for brownies, therefore 1000g – 200g = 800g remaining

25% of 800g = 800 ÷ 4 = 200g

Mr Jones bought a second hand car for £12,400

A year later, it had decreased in value by 15%

What was the value of the car after a year?

Answer : £10,540

10% of 12,400 = £1,240

5%  = half of £1240 = £620

15% = 1240 + 620 = £1,860

Value after a year = 12,400 – 1860 = £10,540

The number of visitors to a theme park in 2021 was 286,000.

The following year, there was a 24 percent increase in visitors.

How many visited the theme park in 2022?

Answer : 354,640 visitors

10% of 286,000 = 28,600

20% = 2 x 28,600 = 57,200

1% of 286,000 = 2,860

4% = 4 x 2860 = 11,440

24% = 57,200 + 11,440 = 68.640

Total number of visitors: 286,000 + 68,640 = 354,640

A library has 16,200 books

55% are fiction and 45% are non-fiction

968 non-fiction books are taken out in one week.

How many non-fiction books are left in the library, from the books which were there at the start of the week? 

Answer : 6,322 non-fiction books

10% of 16,200 = 1,620

40% = 1,620 x 4 = 6,480 books

5% = half of 1,620 = 810

45% = 6,480 + 810 = 7,290

7,290 – 968 = 6,322

In Key Stage 3, the work pupils carry out on percentages, builds upon the percentage skills developed in primary. Students need to be able to solve percent word problems involving interpreting percentages and percentage change as a fraction or decimal; expressing one quantity as a percentage of another; comparing two quantities using percentages; working with percentages greater than 100% and interpreting fractions and percentages as operators.

Jasmine wins £600

She gives 30% to her sister and 20% to her friend.

She keeps the rest.

How much does each person have?

Sister: £180

Friend: £120

Jasmine: £300

She gives 30% to her sister.

10% of £600 = £60

30% = 3 x 60 = £180

She gives 20% to her friend.

20% = 2 x 60 = £120

She must keep 50% for herself, if she has given 30% and 40% away.

50% of 600 =  \frac{1}{2} of 600 = £300

A car is reduced in the sale by 15%

If the original price was £18,500, what is the price of the car now?

Answer: £16,225

10% of 18500 = 1,850

5% = half of 1,850 = £925

15% = 1,850 + 925 = £2,275

New price: 18,500 – 2,275 = £16,225

Sales tax in Florida is 6%

Maisie has bought a pair of jeans, 3 T shirts and a jacket, which came to $150

How much will she have to pay, once she has added on the sales tax?

Answer: $159

1% of 150 = 1.5

6% = 6 x 1.5 = $9

150 + 9 = $159

A packet of biscuits is 300g

As a special offer, the biscuits currently have an extra 15% free.

How many grams of biscuit do you get with the special offer?

Answer : 345g

10% of 300 = 30g

5% = half of 30 = 15g

15% = 30 + 15 = 45g

New weight: 300 + 45 = 345g

Jason is travelling to Birmingham from Manchester.

His average speed is 62 miles per hour

On the return journey, the traffic on the M6 is terrible and his average speed it reduced by 35%

What is his average speed on the return journey?

Answer : 40.3mph

10% of 62 = 6.2mph

30% = 6.2 x 3 = 18.6mph

5% = half of 6.2 = 3.1mph

35% = 18.6 + 3.1 = 21.7mph

62 – 21.7 = 40.3 mph

Mr Andrews bought a car in January 2021 for £15000.

By January 2022 his car had depreciated in value by 20%.

By January 2023, his car had depreciated in value by another 30%.

What was the value of his car in January 2023?

Answer : £8400

January 2022

20% of £15000 = £3000, so the value of the car is £12000.

January 2023

30% of £12000 = £3600, so the value of the car is £8400.

Alternative method – using decimal multiplier

20% decrease means 80% of January 2021 value – decimal multiplier of 0.8

30% decrease means 70% of January 2022 value – decimal multiplier of 0.7

15000 x 0.8 x 0.7 = £8400.

In her half term test, Jasmine did a French test and scored 15 out of 30.

In her next half term test, Jasmine scored 21 out of 30 in her French test.

By what percentage did Jasmine improve?

Answer : 40% improvement

Percentage change

= 21 – 15/15  x 100

= 6/15  x 100 = 40% improvement.

In 2021, a company made a profit of $600000.

In 2022, the same company made a profit of $1350000.

By what percentage had their profit increased?

Answer : 125% improvement

= 1350000 – 600000/600000 x 100

= 750000/600000 x 100 = 125% improvement.

In 2022, Thomas earned £1800 a month for his job.

As part of his annual review in February 2023, he is going to ask for a pay rise of 3.5%.

If the pay rise is agreed, what will Thomas’ annual salary be?

Answer: £22356

3.5% of £1800 = £63

So new monthly salary would be £1863

£1863 x 12 = £22356.

Alternative method 1

£1800 x 12 = £21600

3.5% of £21600 = £756

£21600 + £756 = £22356.

Looking for more word problems practice questions? Take a look at our collection of addition and subtraction word problems , time word problems , money word problems and ratio word problems . Teaching percentages to KS3 or KS4? Check out our percentage worksheets here.

There are different types of percentage problems. If you want to find the percentage of an amount, it can be calculated by writing the percentage as a decimal or a fraction and then multiplying it by the amount.

Pupils in Year 5 held a vote on where to go for their next school trip. The vote was between the zoo and the aquarium. 90 children voted.  40% voted for the zoo How many pupils voted for the aquarium?

1. Calculating a discount when shopping 2. Understanding bank interest rates 3. Understanding your grades in school

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6th Grade Percent Word Problems

Welcome to our 6th Grade Percent Word Problems page. In this area, we have a selection of percentage problem worksheets for 6th graders designed to help children learn to solve a range of percentage problems.

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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:

• general percentage problems;
• solving percentage problems with bar graphs.

Each of the general problem solving sheets has also been split into 2 different worksheets:

• Sheet A which is set at an easier level;
• Sheet B which is set at a harder level;

Some of our worksheets have UK versions, which use £ instead of $.

6th Grade Percentages Problems Worksheets - General Problems

There are 6 problems on each sheet. Sheet A is an easier version and Sheet B is a harder version.

Answer sheets include example working out to solve the problems.

• 6th Grade Percent Word Problems Sheet 6.1A
• PDF version
• 6th Grade Percent Word Problems Sheet 6.1B
• 6th Grade Percent Word Problems Sheet 6.2A
• UK version Worksheet
• UK version Answers
• UK Version PDF
• 6th Grade Percent Word Problems Sheet 6.2B
• UK Version Worksheet
• UK Version Answers
• 6th Grade Percent Word Problems Sheet 6.3A
• 6th Grade Percent Word Problems Sheet 6.3B

6th Grade Bar Graph Percentage Word Problems

These sheets involve using bar graph data to solve different percentage problems.

There is only one version of each sheet, and both sheets are at a similar level of difficulty.

• 6th Grade Bar Graph Percentage Word Problems 6.1
• 6th Grade Bar Graph Percentage Word Problems 6.2

Bar Graph Percentage Word Problems Walkthrough Video

This short video walkthrough shows the problems from our 6th Grade Bar Graph Percentage Word Problems Worksheet 6.2 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

More Recommended Math Worksheets

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

• Basic Percentage Word Problems

These word problems are at a slightly easier level than those on this page.

All the problems involve finding the percentage of a range of numbers and amounts.

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
• 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.

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

These sheets are a great way to introduce ratio of one object to another using visual aids.

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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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Word Problems on Percentage

Word problems on percentage will help us to solve various types of problems related to percentage. Follow the procedure to solve similar type of percent problems.

Word problems on percentage:

1.  In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks.

Let the maximum marks be m.

Ashley’s marks = 83% of m

Ashley secured 332 marks

Therefore, 83% of m = 332

⇒ 83/100 × m = 332

⇒ m = (332 × 100)/83

⇒ m =33200/83

Therefore, Ashley got 332 marks out of 400 marks.

2. An alloy contains 26 % of copper. What quantity of alloy is required to get 260 g of copper?

Let the quantity of alloy required = m g

Then 26 % of m =260 g

⇒ 26/100 × m = 260 g

⇒ m = (260 × 100)/26 g

⇒ m = 26000/26 g

⇒ m = 1000 g

3. There are 50 students in a class. If 14% are absent on a particular day, find the number of students present in the class.

Solution:             

Number of students absent on a particular day = 14 % of 50

                                          i.e., 14/100 × 50 = 7

Therefore, the number of students present = 50 - 7 = 43 students.

4. In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.

Solution:             

Let the total number of apples in the basket be m

12 % of the apples are rotten, and apples in good condition are 66

Therefore, according to the question,

88% of m = 66

⟹ 88/100 × m = 66

⟹ m = (66 × 100)/88

⟹ m = 3 × 25

Therefore, total number of apples in the basket is 75.

5. In an examination, 300 students appeared. Out of these students; 28 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.

The number of students with first division = 28 % of 300

                                                             = 28/100 × 300

                                                             = 8400/100

                                                             = 84

And, the number of students with second division = 54 % of 300

                                                                        = 54/100 × 300

                                                                        =16200/100

                                                                        = 162

Therefore, the number of students who just passed = 300 – (84 + 162)

                                                                           = 54

Questions and Answers on Word Problems on Percentage:

1. In a class 60% of the students are girls. If the total number of students is 30, what is the number of boys?

2. Emma scores 72 marks out of 80 in her English exam. Convert her marks into percent.

Answer: 90%

3. Mason was able to sell 35% of his vegetables before noon. If Mason had 200 kg of vegetables in the morning, how many grams of vegetables was he able to see by noon?

Answer: 70 kg

4. Alexander was able to cover 25% of 150 km journey in the morning. What percent of journey is still left to be covered?

Answer:  112.5 km

5. A cow gives 24 l milk each day. If the milkman sells 75% of the milk, how many liters of milk is left with him?

Answer: 6 l

6.  While shopping Grace spent 90% of the money she had. If she had $ 4500 on shopping, what was the amount of money she spent?

Answer:  $ 4050

Fraction into Percentage

Percentage into Fraction

Percentage into Ratio

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Percentage into Decimal

Decimal into Percentage

Percentage of the given Quantity

How much Percentage One Quantity is of Another?

Percentage of a Number

Increase Percentage

Decrease Percentage

Basic Problems on Percentage

Solved Examples on Percentage

Problems on Percentage

Real Life Problems on Percentage

Application of Percentage

8th Grade Math Practice From Word Problems on Percentage to HOME PAGE

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Percentage Word Problem Worksheets

Percentages can be calculated from fractions and decimals. Although there are many steps to calculate a percentage, it can be simplified a bit. Multiplication is used if you work with a decimal, and division is used to convert a mixed number to a percentage.

The word percentage means 100 percent. For example, 10 percent means 10 out of 100. This can be written as 10 or 10% or as a fraction of 10/100, or as a decimal such as .10. It can look at numbers written in different formats and choose them as potential percentages can help students prepare for tests.

Benefits of Percentage Word Problem Worksheets

Cuemath's interactive math worksheets consist of visual simulations to help your child visualize the concepts being taught, i.e., "see things in action and reinforce learning from it." The percentage word problem worksheets follow a step-by-step learning process that helps students better understand concepts, recognize mistakes, and possibly develop a strategy to tackle future problems and In the Percent Problems Worksheet, we will also practice different types of questions about calculating percentage word problems.

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5.2.1: Solving Percent Problems

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Learning Objectives

• Identify the amount, the base, and the percent in a percent problem.
• Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100, so they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

• The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.
• The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.
• The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price.

You will return to this problem a bit later. The following examples show how to identify the three parts: the percent, the base, and the amount.

Identify the percent, amount, and base in this problem.

30 is 20% of what number?

Percent: The percent is the number with the % symbol: 20%.

Base : The base is the whole amount, which in this case is unknown.

Amount: The amount based on the percent is 30.

Percent=20%

Base=unknown

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Identify the percent, base, and amount in this problem:

What percent of 30 is 3?

The percent is unknown, because the problem states " What percent?" The base is the whole in the situation, so the base is 30. The amount is the portion of the whole, which is 3 in this case.

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (=) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

\[\ \text { Percent } {\color{red}\cdot}\text { Base }{\color{blue}=}\text { Amount } \nonumber \]

In the examples below, the unknown is represented by the letter \(\ n\). The unknown can be represented by any letter or a box \(\ \square\) or even a question mark.

Write an equation that represents the following problem.

\(\ 20 \% \cdot n=30\)

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as \(\ 20 \% \cdot n=30\), you can divide 30 by 20% to find the unknown: \(\ n=30 \div 20 \%\).

You can solve this by writing the percent as a decimal or fraction and then dividing.

\(\ n=30 \div 20 \%=30 \div 0.20=150\)

What percent of 72 is 9?

\(\ 12.5 \% \text { of } 72 \text { is } 9\).

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

\(\ 10 \% \text { of } 72=0.1 \cdot 72=7.2\)

\(\ 20 \% \text { of } 72=0.2 \cdot 72=14.4\)

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

What is 110% of 24?

\(\ 26.4 \text { is } 110 \% \text { of } 24\).

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

18 is what percent of 48?

• \(\ 0.375 \%\)
• \(\ 8.64 \%\)
• \(\ 37.5 \%\)
• \(\ 864 \%\)

Incorrect. You may have calculated properly, but you forgot to move the decimal point when you rewrote your answer as a percent. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Incorrect. You may have used \(\ 18\) or \(\ 48\) as the percent, rather than the amount or base. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Correct. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives \(\ 37.5 \%\).

Incorrect. You probably used 18 or 48 as the percent, rather than the amount or base, and also forgot to rewrite the percent as a decimal before multiplying. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

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• 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.
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• 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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