7 Ways to Write Equations From Word Problems

Translating Word Problems into Mathematical Equations

Word problems can be challenging, but learning to translate them into mathematical equations can make solving them much easier. In this post, we’ll explore 7 ways to write equations from word problems, providing you with a comprehensive guide to improve your problem-solving skills.

1. Identify the Key Elements

When dealing with word problems, it’s essential to identify the key elements, such as the variables, constants, and the relationships between them. Pay attention to the words and phrases that indicate mathematical operations, like “more than,” “less than,” “twice as much,” or “three times as many.”

For example, consider the following word problem:

“Tom has 15 more apples than his friend, Alex. If Alex has 20 apples, how many apples does Tom have?”

In this problem, the key elements are Tom’s apples (variable), Alex’s apples (constant), and the relationship between them (more than).

Writing the Equation

Let’s use the variable “T” to represent Tom’s apples and the constant “A” to represent Alex’s apples. Since Tom has 15 more apples than Alex, we can write the equation:

T = A + 15

Substituting the value of A (20), we get:

T = 20 + 15 T = 35

So, Tom has 35 apples.

🤔 Note: When writing equations, always use variables and constants consistently throughout the problem.

2. Use Mathematical Vocabulary

Word problems often use mathematical vocabulary to describe relationships between variables. Learn to recognize and translate these words into mathematical symbols.

Here are some common examples:

For example, consider the following word problem:

“A bookshelf has 5 shelves, and each shelf can hold 8 books. If the bookshelf is currently empty, how many books can be placed on it in total?”

In this problem, we can use the mathematical vocabulary “times” to represent the relationship between the number of shelves and the number of books per shelf.

Writing the Equation

Let’s use the variable “B” to represent the total number of books. Since each shelf can hold 8 books, and there are 5 shelves, we can write the equation:

B = 5 × 8 B = 40

So, the bookshelf can hold 40 books.

3. Draw a Diagram

Visualizing the problem can help you write an equation. Draw a diagram to represent the problem, labeling the variables and constants.

For example, consider the following word problem:

“A rectangle has a length of 6 cm and a width of 4 cm. What is the area of the rectangle?”

In this problem, we can draw a diagram to represent the rectangle.

Writing the Equation

Let’s use the variable “A” to represent the area of the rectangle. Since the area of a rectangle is equal to the product of its length and width, we can write the equation:

A = length × width A = 6 × 4 A = 24

So, the area of the rectangle is 24 cm².

4. Use Ratios and Proportions

Word problems often involve ratios and proportions. Learn to recognize and write equations using ratios and proportions.

For example, consider the following word problem:

“A recipe for making cookies calls for a ratio of 2:3 of sugar to flour. If you need 4 cups of flour, how many cups of sugar do you need?”

In this problem, we can use the ratio of sugar to flour to write an equation.

Writing the Equation

Let’s use the variable “S” to represent the amount of sugar needed. Since the ratio of sugar to flour is 2:3, we can write the equation:

S/4 = ²⁄₃

Cross-multiplying, we get:

3S = 8 S = ⁸⁄₃ S = 2 ²⁄₃

So, you need 2 ²⁄₃ cups of sugar.

5. Identify the Units

When dealing with word problems, it’s essential to identify the units of measurement. Make sure to include the units in your equation.

For example, consider the following word problem:

“A car travels 250 miles in 5 hours. What is the average speed of the car?”

In this problem, we need to identify the units of measurement for distance (miles) and time (hours).

Writing the Equation

Let’s use the variable “S” to represent the average speed of the car. Since speed is equal to distance divided by time, we can write the equation:

S = distance ÷ time S = 250 miles ÷ 5 hours S = 50 miles/hour

So, the average speed of the car is 50 miles per hour.

6. Use Algebraic Expressions

Word problems often involve algebraic expressions. Learn to recognize and write equations using algebraic expressions.

For example, consider the following word problem:

“A company sells two types of tickets: adult tickets for 15 and child tickets for 10. If the company sells 200 adult tickets and 300 child tickets, what is the total revenue?”

In this problem, we can use algebraic expressions to represent the total revenue.

Writing the Equation

Let’s use the variable “R” to represent the total revenue. Since the revenue from adult tickets is 15 × 200 and the revenue from child tickets is 10 × 300, we can write the equation:

R = 15 × 200 + 10 × 300 R = 3000 + 3000 R = 6000

So, the total revenue is $6000.

7. Check Your Units

Finally, when writing equations, always check your units to ensure they match the problem.

For example, consider the following word problem:

“A water tank can hold 1000 liters of water. If 300 liters of water are already in the tank, what percentage of the tank is filled?”

In this problem, we need to check our units to ensure they match the problem.

Writing the Equation

Let’s use the variable “P” to represent the percentage of the tank filled. Since the amount of water in the tank is 300 liters, and the total capacity is 1000 liters, we can write the equation:

P = (300 ÷ 1000) × 100 P = 30%

So, the tank is 30% filled.

By following these 7 ways to write equations from word problems, you’ll become proficient in translating word problems into mathematical equations, making it easier to solve them. Remember to always identify the key elements, use mathematical vocabulary, draw diagrams, use ratios and proportions, identify the units, use algebraic expressions, and check your units.