Linear Equation Word Problems

Article Contents

Translating Words to Equations
Common Patterns
Step-by-Step Approach
Examples
Practice Problems

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"	$2 x$
"half of a number"	$x /2$
"equals"	$=$

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: $x = 8$

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

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

Translation: $x - 4 = 10$

Solution: $x = 14$

Pattern 3: Multiplication

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

Translation: $3 x = 24$

Solution: $x = 8$

Pattern 4: Unknown on Both Sides

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

Translation: $x + 7 = 12$

Solution: $x = 5$

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

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.

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.

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.

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

Problem 2

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

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

Problem 3

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

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

Comprehensive Guide - Full solving techniques
Simple Equations - Basic equations