Linear Equation Word Problems

Article Contents

1. Translating Words to Equations
2. Common Patterns
3. Step-by-Step Approach
4. Examples
5. Practice Problems

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1. Translating Words to Equations {#translating-words-to-equations}

Word problems describe situations using words instead of math symbols.

Your job: translate the words into an equation.

Common Translations

Words	Math Symbol
"a number plus 3"	$x+3$
"5 subtracted from a number"	$x-5$
"twice a number"	$2x$
"half of a number"	$x/2$
"equals"	$=$

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2. Common Patterns {#common-patterns}

Pattern 1: "Something plus something equals..."

"A number plus 7 equals 15. What is the number?"

Translation: $x+7=15$

Solution: $x=8$

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Pattern 2: "Something minus something equals..."

"A number minus 4 equals 10. What is the number?"

Translation: $x-4=10$

Solution: $x=14$

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Pattern 3: Multiplication

"Three times a number equals 24. What is the number?"

Translation: $3x=24$

Solution: $x=8$

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Pattern 4: Unknown on Both Sides

"7 more than a number equals 12. What is the number?"

Translation: $x+7=12$

Solution: $x=5$

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3. Step-by-Step Approach {#step-by-step-approach}

Step 1: Read the problem carefully

Step 2: Identify what $x$ represents

Step 3: Translate words to math

Step 4: Solve the equation

Step 5: Check your answer in the original problem

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4. Examples {#examples}

Example 1: Simple Addition

Problem: Maria has 12 apples. She buys some more and now has 20 apples. How many did she buy?

Solution:

```

x = apples she bought

12 + x = 20

x = 20 - 12 = 8

```

Maria bought 8 apples.

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Example 2: Subtraction

Problem: Peter had 50 euros. After buying a book, he has 35 euros left. How much did the book cost?

Solution:

```

x = cost of the book

50 - x = 35

x = 50 - 35 = 15

```

The book cost 15 euros.

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Example 3: Unknown in Two Places

Problem: In a classroom, there are 15 students. The number of boys is 3 more than the number of girls. How many boys are there?

Solution:

```

Let g = number of girls

Then boys = g + 3

Total: g + (g + 3) = 15

2g + 3 = 15

2g = 12

g = 6 girls

Boys = 6 + 3 = 9 boys

```

There are 9 boys.

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5. Practice Problems {#practice-problems}

Problem 1

"Tomas had some candies. He gave 5 to his friend and has 12 left. How many did he start with?"

Answer: $x-5=12\Rightarrow x=17$

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Problem 2

"Three times a number is 27. What is the number?"

Answer: $3x=27\Rightarrow x=9$

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Problem 3

"The sum of a number and 8 is 20. What is the number?"

Answer: $x+8=20\Rightarrow x=12$

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• Simple Equations - Basic equations