Solving word problems in elementary school is an essential part of the math curriculum. Here are over 30 math word problems to practice with children, plus expert guidance on how to solve them.
This blog is part of our series of blogs designed for teachers, schools and parents supporting home learning.
What is a word problem?
A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a ‘real-life’ scenario.
This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem.
For example:
Isn’t brilliant arithmetic enough?
In short, no. Students need to build good reading comprehension, even in math. Overtime math problems become increasingly complex and require students to possess deep conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
As students progress through their mathematical education, they will need to be able to apply mathematical reasoning and develop mathematical arguments and proofs using math language. They will also need to be dynamic, applying their math knowledge to a variety of increasingly sophisticated problems.
To support this schools are adopting a ‘mastery’ approach to math
“Teaching for mastery”, is defined with theses component:
- Math teaching for mastery rejects the idea that a large proportion of people ‘just can’t do math’.
- All students are encouraged by the belief that by working hard at math they can succeed.
- Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other.
- Significant time is spent developing deep knowledge of the key ideas that are needed to support future learning. The structure and connections within the mathematics are emphasized, so that students develop deep learning that can be sustained.
(The Essence of Maths Teaching for Mastery, 2016)
Mastery helps children to explore math in greater depth
Fluency in arithmetic is important; however, with this often lies the common misconception that once a child has learned the number skills appropriate to their grade level/age, they should be progressed to the next grade level/age of number skills.
The mastery approach encourages exploring the breadth and depth of these math concepts (once fluency is secure) through reasoning and problem solving.
How to teach children to solve word problems?
Here are two simple strategies that can be applied to many word problems before solving them.
- What do you already know?
- How can this problem be drawn/represented pictorially?
Let’s see how this can be applied to word problems to help achieve the answer.
Solving a simple word problem
There are 28 students in a class.
The teacher has 8 liters of orange juice.
She pours 225 milliliters of orange juice for every student.
How much orange juice is left over?
1. What do you already know?
- There are 1,000ml in 1 liter
- Pours = liquid leaving the bottle = subtraction
- For every = multiply
- Left over = requires subtraction at some point
2. How can this problem be drawn/represented pictorially?
The bar model, also known as strip diagram, is always a great way of representing problems. However, if you are not familiar with this, there are always other ways of drawing it out.
Read more: What is a bar model
For example, for this question, you could draw 28 students (or stick man x 28) with ‘225 ml’ above each one and then a half-empty bottle with ‘8 liters’ marked at the top.
Now to put the math to work. This is a 5th grade multi-step problem, so we need to use what we already know and what we’ve drawn to break down the steps.
Solving a more complex, mixed word problem
Mara is in a bookshop.
She buys one book for $6.99 and another that costs $3.40 more than the first book.
She pays using a $20 bill.
What change does Mara get? (What is the remainder?)
1. What do you already know?
- More than = add
- Using decimals means I will have to line up the decimal points correctly in calculations
- Change from money = subtract
2. How can this problem be drawn/represented pictorially?
See this example of bar modelling for this question:
Now to put the math to work using what we already know and what we’ve drawn to break down the steps.
Mara is in a bookshop.
She buys one book for $6.99 and another that costs $3.40 more than the first book. 1) $6.99 + ($6.99 + $3.40) = $17.38
She pays using a $20 bill.
What change does Mara get? 2) $20 – $17.38 = $2.62
Math Word Problems For Kindergarten to Grade 5
The more children learn about math as they go through elementary school, the trickier the word problems they face will become.
Below you will find some information about the types of word problems your child will be coming up against on a year by year basis, and how word problems apply to each elementary grade.
Word problems in kindergarten
Throughout kindergarten a child is likely to be introduced to word problems with the help of concrete resources (manipulatives, such as pieces of physical apparatus like coins, cards, counters or number lines) to help them understand the problem.
An example of a word problem for kindergarten would be
Chris has 3 red bounce balls and 2 green bounce balls. How many bounce balls does Chris have in all?
Word problems 1st grade
First grade is a continuation of kindergarten when it comes to word problems, with children still using concrete resources to help them understand and visualize the problems they are working on
An example of a word problem for first grade would be:
A class of 10 children each have 5 pencils in their pencil cases. How many pencils are there in total?
Word problems in 2nd grade
In second grade, children will move away from using concrete resources when solving word problems, and move towards using written methods. Teachers will begin to demonstrate the adding and subtracting within 100, adding up to 4- two-digit numbers at a time.
This is also the year in which 2-step word problems will be introduced. This is a problem which requires two individual calculations to be completed.
Second grade word problem: Geometry properties of shape
Shaun is making shapes out of plastic straws.
At the vertices where the straws meet, he uses blobs of modeling clay to fix them together
Here are some of the shapes he makes:
| Shape | Number of straws | Number of blobs of modeling clay |
| A | 4 | 4 |
| B | 3 | 3 |
| C | 6 | 6 |
One of Sean’s shapes is a triangle. Which is it? Explain your answer.
Answer: shape B as a triangle has 3 sides (straws) and 3 vertices, or angles (clay)
Second grade word problem: Statistics
2nd grade is collecting pebbles. This pictogram shows the different numbers of pebbles each group finds.
Word problems in 3rd grade
At this stage of their elementary school career, children should feel confident using the written method for addition and subtraction. They will begin multiplying and dividing within 100.
This year children will be presented with a variety of problems, including 2-step problems and be expected to work out the appropriate method required to solve each one.
3rd grade word problem: Number and place value
My number has four digits and has a 7 in the hundreds place.
The digit which has the highest value in my number is 2.
The digit which has the lowest value in my number is 6.
My number has 3 fewer tens than hundreds.
What is my number?
Answer: 2,746
Word problems in 4th grade
One and two-step word problems continue in fourth grade, but this is also the year that children will be introduced to word problems containing decimals.
Fourth grade word problem: Fractions and decimals
Stan, Frank and John are washing their cars outside their houses.
Stan has washed 0.5 of his car.
Frank has washed 1/5 of his car.
Norm has washed 2/5 of his car.
Who has washed the most?
Explain your answer.
Answer: Stan (he has washed 0.5 whereas Frank has only washed 0.2 and Norm 0.4)
Word problems in 5th grade
In fifth grade children move on from 2-step word problems to multi-step word problems. These will include fractions and decimals.
Here are some examples of the types of math word problems in fifth grade will have to solve.
5th grade word problem – Ratio and proportion
The Angel of the North is a large statue in England. It is 20 meters tall and 54 meters wide.
Ally makes a scale model of the Angel of the North. Her model is 40 centimeters tall. How wide is her model?
Answer: 108cm
Fifth grade word problem – Algebra
Amina is making designs with two different shapes.
She gives each shape a value.
Calculate the value of each shape.
Answer: 36 (hexagon) and 25.
Fifth grade word problem: Measurement
There are 28 students in a class.
The teacher has 8 liters of orange juice.
She pours 225 milliliters of orange juice for every student.
How much orange juice is left over?
Answer: 1.7 liters or 1,700ml
Topic based word problems
The following examples give you an idea of the kinds of math word problems your child will encounter in elementary school
Place value word problem fourth grade
This machine subtracts one hundredth each time the button is pressed. The starting number is 8.43. What number will the machine show if the button is pressed six times? Answer: 8.37
Download free number and place value word problems for grades 2, 3, 4 and 5
Addition and subtraction word problem grade 2
Sam has 64 sweets. He gets given 12 more. He then gives 22 away. How many sweets is he left with? Answer: 54
Download free addition and subtraction word problems for for grades 2, 3, 4 and 5
Addition word problem grade 2
Sammy thinks of a number. He subtracts 70. His new number is 12. What was the number Sammy thought of? Answer: 82
Subtraction word problem fifth grade
The temperature at 7pm was 4oC. By midnight, it had dropped by 9 degrees. What was the temperature at midnight? Answer: -5oC
Multiplication word problem third grade
Eggs are sold in boxes of 12. The egg boxes are delivered to stores in crates. Each crate holds 9 boxes. How many eggs are in a crate? Answer: 108
Download free multiplication word problems for grades 2, 3, 4 and 5.
Division word problem fifth grade
A factory produces 3,572 paint brushes every day. They are packaged into boxes of 19. How many boxes does the factory produce every day? Answer: 188
Download free division word problems for grades 2, 3, 4 and 5.
Free resource: Use these four operations word problems to practice addition, subtraction, multiplication and division all together.
Fraction word problem fourth grade
At the end of every day, a chocolate factory has 1 and 2/6 boxes of chocolates left over. How many boxes of chocolates are left over by the end of a week? Answer: 9 and 2/6 or 9 and 1/3
Download free fractions and decimals word problems for grades 2, 3, 4 and 5.
Money word problem second grade
Lucy and Noor found some money on the playground at recess. Lucy found 2 dimes and 1 penny, and Noor found 2 quarters and a dime. How many cents did Lucy and Noor find? Answer: Lucy = $0.21, Noor = $0.60; $0.21 + $0.61 = $0.81
Area word problem 3rd grade
A rectangle measures 6cm by 5cm.
What is its area? Answer: 30cm2
Perimeter word problem 3rd grade
The swimming pool at the Sunshine Inn hotel is 20m long and 7m wide. Mary swims around the edge of the pool twice. How many meters has she swum? Answer: 108m
Ratio word problem 5th grade (crossover with measurement)
A local council has spent the day painting double yellow lines. They use 1 pot of yellow paint for every 100m of road they paint. How many pots of paint will they need to paint a 2km stretch of road? Answer: 20 pots
PEMDAS word problem fifth grade
Draw a pair of parentheses in one of these calculations so that they make two different answers. What are the answers?
50 – 10 × 5 =
50 – 10 × 5 =
Volume word problem fifth grade
This large cuboid has been made by stacking shipping containers on a boat. Each individual shipping container has a length of 6m, a width of 4m and a height of 3m. What is the volume of the large cuboid? Answer: 864m3
Remember: The word problems can change but the math won’t
It can be easy for children to get overwhelmed when they first come across word problems, but it is important that you remind them that while the context of the problem may be presented in a different way, the math behind it remains the same.
Word problems are a good way to bring math into the real world and make math more relevant for your child. So help them practice, or even ask them to turn the tables and make up some word problems for you to solve.
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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?}
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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?}
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mathrm{Bob’s:age:is:twice:that:of:Barry’s.:Five:years:ago,:Bob:was:three:times:older:than:Barry.:Find:the:age:of:both.}
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mathrm{Two:men:who:are:traveling:in:opposite:directions:at:the:rate:of:18:and:22:mph:respectively:started:at:the:same:time:at:the:same:place.:In:how:many:hours:will:they:be:250:apart?}
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mathrm{If:2:tacos:and:3:drinks:cost:12:and:3:tacos:and:2:drinks:cost:13:how:much:does:a:taco:cost?}
Frequently Asked Questions (FAQ)
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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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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.
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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.
word-problems-calculator
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На основании Вашего запроса эти примеры могут содержать грубую лексику.
На основании Вашего запроса эти примеры могут содержать разговорную лексику.
Often this is enough and the problem is over.
Estimates suggest that the size of the problem is over $500 billion annually.
And when you think the problem is over, it’s not.
First, I don’t think the Greece problem is over yet.
Does it mean the problem is over?
Drink this… before bed… and when you wake in the morning, problem is over.
They’ve managed to nearly completely dry out the supply in the US, which, to some people, means the problem is over.
Ему удалось почти полностью прекратить продажи флакки в США, и некоторых думают, что проблема решена.
And if Sweden, as its legislation perfectly well allows it to do, and as it has done in other cases, questions Mr Assange at the Embassy of Ecuador in London, or interrogates him via Skype tomorrow, this problem is over.
И если Швеция, как ей прекрасно позволяет ее законодательство и как она уже делала в других случаях, допросит сеньора Ассанжа в посольстве Эквадора в Лондоне или допросит его по Skype, завтра эта проблема будет исчерпана.
Well, now that problem is over!
Другие результаты
Many experts say the problem is over-diagnosed, and that only extreme cases should have a formal diagnosis.
The steel sector’s major problem is over-capacity.
As he sees it, the main problem is over-bureaucratisation.
The main problem is not over-fishing, but the workings of global criminal networks.
The real problem is an over-valued European sovereign bond market.
The problem is largely over, and most OECD countries are running fiscal surpluses.
Проблема в целом решена, и у большинства стран ОЭСР наблюдается активное сальдо бюджета.
Another problem is the over-dependence on the welfare from other regions, especially from Hong Kong.
What is most remarkable is how differently the financial problem is perceived over here.
Поразительно то, насколько иначе воспринимают здесь финансовую проблему.
The major root cause of all problems is undoubtedly — over thinking.
Мы работаем с главной причиной всех проблем — мышлением.
This problem is all over the world as you well know.
The problem is that over time they become infected and wear out, and the bone around them collapses.
Проблема состоит в том, что со временем они инфицируются и изнашиваются, а костная ткань вокруг них разрушается.
Результатов: 84974. Точных совпадений: 9. Затраченное время: 1691 мс
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Справка и о нас
Индекс слова: 1-300, 301-600, 601-900
Индекс выражения: 1-400, 401-800, 801-1200
Индекс фразы: 1-400, 401-800, 801-1200
Though the majority of ACT math problems use diagrams or simply ask you to solve given mathematical equations, you will also see approximately 15-18 word problems on any given ACT (between 25% and 30% of the total math section). This means that knowing how best to deal with word problems will help you significantly when taking the test. Though there are many different types of ACT word problems, most of them are not nearly as difficult or cumbersome as they may appear.
This post will be your complete guide to ACT word problems: how to translate your word problems into equations and diagrams, the different types of word problems you’ll see on the test, and how best to go about solving your word problems for test day.
What Are Word Problems?
A word problem is any problem that is based mostly or entirely on written description and does not provide you with an equation, diagram, or graph. You must use your reading skills to translate the words of the question into a workable math problem and then solve for your information.
Word problems will show up on the test for a variety of reasons. Most of the time, these types of questions act to test your reading and visualization skills, as well act as a medium to deliver questions that would otherwise be untestable. For instance, if you must determine the number of sides of an unknown polygon based on given information, a diagram would certainly give the game away!
Translating Word Problems Into Equations or Drawings
In order to translate your word problems into actionable math equations that you can solve, you’ll need to know and utilize some key math terms. Whenever you see these words, you can translate them into the proper action. For instance, the word “product” means “the value of two or more values that have been multiplied together,” so if you need to find “the product of a and b,” you’ll need to set up your equation with $a * b$.
|
Key Terms |
Mathematical Action |
|
Sum, increased by, added to, total of |
+ |
|
Difference, decreased by, subtracted from |
— |
|
Product, times |
* or x |
|
Divided by |
/ or ÷ |
|
Equals, is, are, equivalent, same |
= |
|
Is less than |
< |
|
Is greater than |
> |
|
Is less than or equal to |
≤ |
|
Is greater than or equal to |
≥ |
Let’s take a look at this in action with an example problem:
We have two different cable companies that each have different rates for installation and different monthly fees. We are asked to find out how many months it will take for the cost for each company to be the «same,» which means we must set the two rates equal.
Uptown Cable charges 120 dollars for installation plus 25 dollars a month. We do not know how many months we’re working with, so we will have:
$120 + 25x$
Downtown Cable charges 60 dollars for installation and 35 dollars per month. Again, we don’t know how many months we’re working with, but we know they will be the same, so we will have:
$60 + 35x$
And, again, because we are finding the amount of months when the cost is the «same,» we must set our rates equal.
$120 + 25x = 60 + 35x$
From here, we can solve for $x$, since it is a single variable equation.
[Note: the final answer is G, 6 months]
Learning the language of ACT word problems will help you to unravel much of the mystery of these types of questions.
Typical ACT Word Problems
ACT word problems can be grouped into two major categories: word problems where you must simply set up an equation and word problems in which you must solve for a specific piece of information.
Word Problem Type 1: Setting Up an Equation
This is the less common type of word problem on the test, but you’ll generally see it at least once or twice. You’ll also usually see this type of word problem first. For this type of question, you must use the given information to set up the equation, even though you don’t need to solve for the missing variable.
Almost always, you’ll see this type of question in the first ten questions on the test, meaning that the ACT test-makers consider them fairly “easy.” This is due to the fact that you only have to provide the set-up and not the execution.
We consider a “profit” to be any money that is gained, so we must always subtract our costs from our earnings. We know that Jones had to invest 10 million starting capital, so he is only making a profit if he has earned more than 10 million dollars. This means we can eliminate answer choices C, D, and E, as they do not account for this 10 million.
Now each boat costs Jones 7,000 dollars to make and he sells them for 20,000. This means that he earns a profit of:
$20,000 — 7,000$
$13,000$ per boat.
If $x$ represents our number of boats, then our final equation will be:
$13,000x — 10,000,000$
Our final answer is A, $13,000x — 10,000,000$
Word Problem Type 2: Solving for Your Information
Other than the few set-up word questions you’ll see, the rest of your ACT word problem questions will fall into this category. For these questions, you must both set up your equation and solve for a specific piece of information.
Most (though not all) word problem questions of this type will be scenarios or stories covering all sorts of ACT math topics, including averages, single variable equations, and probabilities, among others. You almost always must have a solid understanding of the math topic in question in order to solve the word problem on the topic.
This question is a rare example of a time in which not every piece of given information is needed to solve the problem. For most ACT word questions, all your given information will come into play at some point, but this is not the case here (though you can use all of your information, should you so choose).
For example, we are told that 25% of a given set of jelly beans are red. 25% translates to $1/4$ because 25% is the same as $25/100$ (or $1/4$). If we are being asked to find how many jelly beans are NOT red, then we know it would be $3/4$ because 100% is the same as 1, and 1 — $1/4$ = $3/4$.
So we didn’t need to know that there were 400 jellybeans to know that our final answer is H, $3/4$.
Alternatively, we could use all of our given information and find 25% of 400 in order to find the remaining jelly beans.
$400 * {1/4}$ or $400/4$
$100$
If 100 jellybeans are red, then 400 — 100 = 300 jelly beans are NOT red. This means that the not-red jelly beans make up,
$300/400$
$3/4$ of the total number of jelly beans.
Again, our final answer is H, $3/4$
You might also be given a geometry problem as a word problem, which may or may not be set up with a scenario as well.
Geometry questions will be presented as word problems typically because the test-makers felt the problem would be too easy to solve had you been given a diagram.
The test-makers didn’t give us a diagram, so let’s make ourselves one and fill it in with what we know so far.
We know from our studies of parallelograms that opposite side pairs will be equal, so we know that the opposite side of our given will also be 12.
Now we can use this information to subtract from our total perimeter.
$72 — 12 — 12$
$48$
Again, opposite sides will be equal and we know that the sum of the two remaining sides will be 48. This means that each remaining side will be:
$48/2$
$24$
Now we have four sides in the pairings of 12 and 24.
Our final answer is C, 12, 12, 24, 24.
Now, how do we put our knowledge to its best effect? Let’s take a look.
ACT Math Strategies for Your Word Problems
Though you’ll see word problems on a myriad of different types of ACT math topics, there are still a few techniques you can apply to solve your word problems as a whole.
#1: Draw It Out
Whether your problem is a geometry problem or an algebra problem, sometimes making a quick sketch of the scene can help you understand what, exactly, you’re working with. For instance, let’s look at how a picture can help you solve a ratio/division problem:
Let’s start by first drawing our sandwich and Jerome’s portion of it.
Now let’s divvy off Kevin’s portion and, by the remainder, Seth’s as well.
By seeing the problem visually, we can see that the ratio of Jerome’s share, to Kevin’s, to Seth’s will go in descending order of size. This let’s us eliminate answer choices A, B, and C, and leaves us with answer choices D and E.
Just by drawing it out and using process of elimination, and without knowing anything else about ratios, we have a 50-50 shot of guessing the right answer. And, again, without knowing anything else about fractions or ratios, we can make an educated guess between the two options. Since Jerome’s share doesn’t look twice as large as Kevin’s, our answer is probably not E.
This leaves us with our final answer D, 3:2:1.
[Note: for a breakdown on how to solve this problem using fractions and ratios instead of using a diagram and educated guessing, check out our guide to ACT fractions and ratios.]
As for geometry problems, remember—you’re often given a word problem as a word problem because it would be too simple to solve had you had a diagram to work with from the get-go. So take back the advantage and draw the picture yourself. Even a quick and dirty sketch can help you visualize the problem much easier than you can in your head and help keep all your information clear.
#2: Memorize Important Terms
If you’re not used to translating English words into mathematical equations, then ACT word problems can sound like so much nonsense and leave you floundering to set up the proper equation. Look to the chart and learn how to translate your keywords into their math equivalents. Doing so will help you to understand exactly what the problem is asking you to find.
There are free ACT math questions available online, so memorize your terms and then practice on real ACT word problems to make sure you’ve got your definitions down and can apply them to real problems.
#3: Underline and Write Out the Key Information
The key to solving a word problem is bringing together all the relevant pieces of given information and putting them in the right places. Make sure you write out all your givens on the diagram you’ve drawn (if the problem calls for a diagram) and that all your moving pieces are in order.
One of the best ways to keep all your pieces straight is to underline them in the problem and then write them out yourself before you set up your equation, so take a moment to perform this step.
#4: Pay Close Attention to Exactly What Is Being Asked of You
Little is more frustrating than solving for the wrong variable or writing in your given values in the wrong places. And yet this is entirely too easy to do when working with word problems.
Make sure you pay strict attention to exactly what you’re meant to be solving for and exactly what pieces of information go where. Are you looking for the area or the perimeter? The value of $x$ or $x + y$? Better to make sure before you start what you’re supposed to find than realize two minutes down the line that you have to solve the problem all over again.
#5: Brush Up on Any Specific Math Topic in Which You Feel Weak
You are likely to see both diagram/equation problems and word problems for any given ACT math topic on the test. Many of the topics can swing either way, which is why there are so many different types of word problems and why you’ll need to know the ins and outs of any particular math topic in order to solve its corresponding word problem. For example, if you don’t know how to properly set up a system of equations problem, you will have a difficult time of it when presented with a word problem on the topic.
So understand that solving a word problem is a two-step process: it requires you to both understand how word problems themselves work and to understand the math topic in question. If you have any areas of mathematical weakness, now is a good time to brush up on them, or else the word problem might be trickier than you were expecting.
All set? Time to shine!
Test Your Knowledge
Now to put your word problem know-how to the test with real ACT math problems.
Answers: K, C, A, E
Answer Explanations:
1) First, let us make a sketch of what we have, just so we can keep our measurements straight. We know we have two triangles, one smaller than the other, and the hypotenuse of the smaller triangle is 5.
Now our triangles are in a ratio of 2:5, so if the hypotenuse of the smaller triangle is 5, we can find the hypotenuse of the larger triangle by setting them up in a proportion.
$2/5 = 5/x$
$2x = 25$
$x = 12.5$
Our final answer is K, 12.5.
2) Because we are dealing with a hypothetical number that is increasing and decreasing based on percentage, we can solve this problem in one of two ways—by using algebra or by plugging in our own numbers.
Solving Method 1: Algebra
If we assign our hypothetical number as $x$, we can say that $x$ is increased by 25% by saying:
$x + 0.25x$
Which gives us:
$1.25x$
Now, we can decrease this value by 20% by saying:
$1.25x — (1.25x * 0.2)$
$1.25x — 0.25x$
This leaves us with:
$1x$ or 100% of our original number.
Our final answer is C, 100%.
Solving Method 2: Plugging in Numbers
Alternatively, we can use the same basic process, but make it a little simpler by using numbers instead of variables.
Let’s say our original number is 100. (Why 100? Why not! Our number can literally be anything and 100 is an easy number to work with.)
So if we need to increase 100 by 25%, we first need to find 25% of 100 and then add that to 100.
$100 + (0.25)100$
$100 + 25$
$125$
Now we need to decrease this value by 20%, so we would say:
$125 — (0.2)125$
$125 — 25$
$100$
We are left with the same number we started with, which means we are left with 100% of the number we started with.
Again, our final answer is C, 100%.
3) Let’s first begin by drawing a picture of our scene. We know that one vertex of the square is at (3, 0), so we can mark it on a coordinate plane.
Now, we are told that each side of the square is 3 cm long. To make life simple, we can start by marking all the possible vertexes attached to our known vertex at (3, 0) straight up, down, and side to side. If no answers match, we can then look to vertexes at different angles.
Our possible vertexes are:
(0, 0), (6, 0), 3, 3) and (3, -3)
One of our possible vertexes is at (6, 0 and this matches one of our answer choices, so we can stop here.
Our final answer is A, (6, 0).
4) We are told that Ms. Lopez throws out the lowest test score and then averages the remaining scores. Because Victor’s scores are already in ascending order, we can throw out the first score of 62.
Now to find the average of the remaining 4 scores, let us add them together and then divide by the number of scores.
$(78 + 83 + 84 + 93)/4$
$338/4$
$84.5$
Our final answer is E, 84.5.
A round of applause to your success!
Picture: John Morris/Flickr
The Take-Aways
Word problems comprise a significant portion of the ACT, so it’s a good idea to understand how they work and how to translate the words into a proper equation. But remember that translating your word problems is still only half the battle.
You must also supplement this knowledge of how to solve word problems with a solid understanding of the math topic in question. For example, it won’t do a lot of good if you can translate a probability word problem if you don’t understand exactly how probabilities work. So be sure to not only learn how to approach your word problems, but also hone your focus on any math topics you feel you need to improve upon. You can find links to all of our ACT math topic guides here to help your studies.
What’s Next?
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About the Author
Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time.
Solving Word Problems in Algebra
Writing Standard Form Equations
We’ve studied word problems that allow for you to write an equation in slope intercept form. How do we know when a problem should be solved using an equation written in standard form?
As you are reading and analyzing the word problem, if you find that
you can set up an addition problem, and you have a set total (constant),
then you will be able to write an equation in standard form.
Let’s look at a couple of examples.
Your school is sponsoring a pancake dinner to raise money for a field trip. You estimate that 200 adults and 250 children will attend. Let x represent the cost of an adult ticket and y represent the cost of a child ticket.
- Write an equation that can be used to find what ticket prices to set in order to raise $3800.
Solution
First, think about what we know.
We know that you want to raise $3800. This is a constant. Therefore, it will be C in your standard form equation.
We also know that in order to find our total, we need to multiply the number of people by the cost of the ticket. If we add the adult tickets and children tickets together, we will have a total.
Ax + By = C
200x + 250y = 3800
Here’s a more thorough explanation.
Word Problems Are Tough!
I know how difficult it is to not only learn the skill, but then to be
able to apply the skill. It is hard and unfortunately, it just takes
practice!
If you are struggling with this concept, then check out the Algebra Class E-course.
Within this E-course, you will find a lot of word problems that will
not only help as you study for your tests, but that will also help you
in real-life situations.
Often times, text book word problems are
pretty «far out»; however Algebra Class word problems are more realistic
and easy to relate to every day living.
For more information, click here.
Let’s look at one more example.
Example 2: Another Word Problem!
You are running a concession stand at the basketball game. You sell hot dogs for $1 and sodas for $0.50. At the end of night, you made $200. Let x represent the number of hot dogs sold and y represent the number of sodas sold.
- Write an equation that can be used to determine how many hot dogs and how many sodas were sold.
Solution
Think about what you know.
We know that our total for the end of the night was $200; therefore, it is our constant (C) in the equation.
We also have information for the price of the hot dogs and the price of the sodas.
Ax + By = C
1x + 0.50y = 200
Here’s another way to think of it!
I know it’s hard to imagine when you will need to use this skill, or
even how to solve problems written in this form.
You will be writing
these equations and solving them when you get to the Systems of Equations Unit. So, stick with me — it will all come together and make sense.
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