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Word Problems Involving One Step Linear Equations

A word problem requires you to find an answer from the facts of the problem. There are a few steps you should follow to successfully solve a word problem.

1. Understand what the problem is asking

• Do you understand all the words used in the problem?
• What are you asked to find?
• Can you restate the problem in your own words?
2. Make a plan.
• Pick an approach and give it a try.
• Guess and check.
• Look for a pattern.
• Draw a picture.
• Use a chart.
• Set up variables and solve an equation.

3. Put the plan into action.

• Make sure your answer makes sense in the context of the problem.

Phrases to indicate which operation to use

You can find clues in the words and phrases used in word problems to decide which operations you should use to solve them. Some of the phrases and their matching operations are listed here.

Words that indicate problems using addition (+)

Sum

Together

Total

All together

Combined

x more than a number

x greater than a number

x units longer than/ older than/ taller than/ heavier than a quantity

Words that indicate problems using subtraction (-)

Difference

Left

Amount left

Less than

Diminished by

Decreased by

Shorter than/ younger than/ lighter than

Words that indicate problems using multiplication (x or *)

Product

Times as many

As much as

Times as long as/ as old as/ as tall as/ as heavy as a quantity

Words that indicate problems using division (/)

Quotient

For each

For every

The quotient of a number and

Divided by a number

How to solve addition word problems

When you find a word problem that requires a one-step linear equation involving addition, you will be adding two numbers together.

Example 1

Sarah and Matt love dogs. Sarah has 3 dogs and Matt has 5 dogs. How many total dogs do Sarah and Matt have combined?

This word problem is pretty simple. It is asking for the total number of dogs:

$3+5=8$

The answer is 8 dogs.

Example 2

Not all word problems are as straightforward as the previous one.

Sarah and Matt love animals. Sarah has 3 dogs, 2 cats, and 4 birds. Matt has 5 dogs, 3 cats, and 2 birds. How many cats do Sarah and Matt have all together?

There are a number of animals mentioned, and six numbers mentioned. It's important to read the words of the math problem. You might be tempted to add up all the animals together since it is an addition problem, but if you read closely, you are only asked to add up the total number of cats, which is:

$2+3=5$

The answer is 5 cats.

Example 3

Of course, there are problems with much larger numbers.

Terry makes a barbecue with 582 bricks. His neighbor, Denise, makes a barbecue with 657 bricks. How many total bricks do their two barbecues have?

This is a simple problem with greater numbers than the previous ones.

$582+657=1239$

The answer is 1239 bricks.

Note that the answers to word problems are not just the numbers, but the units that the numbers represent. Not just 1239, but 1239 bricks.

How to solve subtraction word problems

When you find a word problem that requires a one-step linear equation involving subtracting, you will be subtracting one number from another.

Example 4

Monica and Jamal love pizza. One day at lunch, Monica eats 6 pieces of pizza and Jamal eats 4 pieces of pizza. How many more pieces of pizza did Monica eat than Jamal?

This word problem is pretty simple since it involves just two numbers and basic subtraction.

$6-4=2$

Monica ate 2 more pieces of pizza than Jamal.

Example 5

Subtraction problems can also be more complex, as with addition problems.

Monica and Jamal love pizza. On Monday, Monica ate 3 pieces of pizza. On Tuesday, she ate 5 pieces of pizza. On Wednesday, she ate 4 pieces of pizza. Jamal ate 6 pieces of pizza on Monday, 4 pieces of pizza on Tuesday, and 8 pieces of pizza on Wednesday. How many more pieces of pizza did Jamal eat on Wednesday?

Again, you have to carefully read the question at the end of the word problem to make sure you choose the right numbers to subtract.

$8-4=4$

Jamal ate 4 more pieces of pizza than Monica on Wednesday.

Example 6

Subtraction problems can also have much larger numbers involved.

Luis and Dana both love books. They own many, many books. Luis owns 1,348 books and Dana owns 1,922 books. How many more books does Dana own than Luis?

This is a simple problem. It just has larger numbers to subtract.

$1922-1348=574$

Dana owns 574 more books than Luis.

How to solve multiplication word problems

When you find a word problem that requires a one-step linear equation involving multiplication, you will be multiplying two numbers.

Example 7

Trina runs 4 miles every day except Tuesday. How many miles does she run in one week?

This problem does not provide both numbers, but you can easily figure out that one day less than a week is 6 days.

$4×6=24$

Trina runs 24 miles every week.

Example 8

Multiplication problems can involve fractions or decimals.

Michael is writing a novel. He writes 3,000 words every other week. On the opposite weeks, he writes half that. How many words does he write on the off weeks?

$3000×\frac{1}{2}=1500$

Michael writes 1500 words on the off weeks.

How to solve division word problems

When you find a word problem that requires a one-step linear equation involving multiplication, you will be dividing two numbers.

Example 9

Dalvin scored 18 points in 6 football games. How many points did he score on average in each football game?

To get an average, you know you have to divide the total number of points by the number of games.

$18÷6=3$

Dalvin scored an average of 3 points per game.

Example 10

Jessica has 12 cookies. She wants to give them all to the friends who are visiting her. She has 3 friends visiting her. How many cookies does each friend get?

This is a basic division problem.

$12÷3=4$

Each friend gets 4 cookies.

Get help learning about word problems involving one-step linear equations

Word problems can cause confusion when students have learned to solve basic linear equations without thinking about what the numbers might mean. But they are very helpful for just that reason. If your student is struggling with solving word problems, connect them with a math tutor who can show them the ropes. Their tutor can walk them through even the most complex word problems to find keywords and figure out what the problem is asking for, making the math part easier. Contact the Educational Directors at Varsity Tutors today to get your student signed up with a qualified tutor.

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