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Reducing word problems to linear equations

Reducing a word problem means converting the given statements into two linear equations in two variables.

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Student-friendly explanation

In such problems, the words describe two unknown quantities and two conditions. The first task is to choose variables for the unknowns and turn the statements into equations. After that, the pair can be solved by any suitable algebraic method.

How to write this in exams

  1. 1

    Start with the exact idea

    Reducing a word problem means converting the given statements into two linear equations in two variables.

  2. 2

    Then show how to use it

    1. Read the problem carefully. 2. Choose variables for the unknowns. 3. Convert each statement into an equation. 4. Solve the pair. 5. Check whether the final answer fits the story.

  3. 3

    Add one concrete example

    If the sum of two numbers is 20 and their difference is 4, we can write x + y = 20 and x - y = 4.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to use one variable for both quantities. That makes the two unknowns indistinguishable and the equations impossible to interpret.

Definition

Reducing a word problem means converting the given statements into two linear equations in two variables.

Example

If the sum of two numbers is 20 and their difference is 4, we can write x + y = 20 and x - y = 4.

Rule to remember

Use two unknowns for two conditions, and translate keywords like sum, difference, total, more than, and less than into equations carefully.

Memory hook

Words first, equations next, answer last.

Examples and method

Worked example

For 'The sum of two numbers is 20 and their difference is 4', let x and y be the numbers. Then x + y = 20 and x - y = 4. Solving gives x = 12 and y = 8.

Method to apply

1. Read the problem carefully. 2. Choose variables for the unknowns. 3. Convert each statement into an equation. 4. Solve the pair. 5. Check whether the final answer fits the story.

Diagram support

A small table with 'given condition' and 'equation formed' can help students organise the translation step.

How CBSE asks it

The exam often gives age, number, money, or speed problems and asks students to form equations before solving them.

Avoid common mistakes

Common confusion

Students sometimes choose the wrong variables or translate the same statement twice instead of forming two different equations.

Common wrong answer

A common wrong answer is to use one variable for both quantities. That makes the two unknowns indistinguishable and the equations impossible to interpret.

Exam tip

Read the problem twice: once to choose variables and once to catch the two separate conditions.

Quick check

What is the first useful step when converting a word problem into a pair of linear equations?

The first useful step is to choose clear variables for the unknown quantities. After that, each statement is translated into one equation based on the given information.

Answer writing and exam use

1-mark answer

Reducing a word problem means converting the given statements into two linear equations in two variables.

2-mark answer

Reducing a word problem means converting the given statements into two linear equations in two variables. Use two unknowns for two conditions, and translate keywords like sum, difference, total, more than, and less than into equations carefully. If the sum of two numbers is 20 and their difference is 4, we can write x + y = 20 and x - y = 4.

3-mark answer

In such problems, the words describe two unknown quantities and two conditions. The first task is to choose variables for the unknowns and turn the statements into equations. After that, the pair can be solved by any suitable algebraic method. Use two unknowns for two conditions, and translate keywords like sum, difference, total, more than, and less than into equations carefully. For 'The sum of two numbers is 20 and their difference is 4', let x and y be the numbers. Then x + y = 20 and x - y = 4. Solving gives x = 12 and y = 8. The exam often gives age, number, money, or speed problems and asks students to form equations before solving them. A common wrong answer is to use one variable for both quantities. That makes the two unknowns indistinguishable and the equations impossible to interpret.
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