Concept Overview
Linear equation word problems turn real situations into equations.
The main skill is choosing a variable and translating words into algebra.
Linear Equations — Age, Digit & Perimeter Problems explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Linear equation word problems turn real situations into equations.
The main skill is choosing a variable and translating words into algebra.
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Age, digit, and perimeter problems are common because they test both reading and equation solving.
A word problem should be read slowly before writing an equation.
Choose a variable for the unknown quantity. Then express other related quantities using that variable.
Age problems often compare present ages, past ages, or future ages.
Digit problems use place value. A twigit number with tens digit a and ones digit b is 10.
Perimeter problems use shape formulas, then form an equation from the given perimeter.
Meaning: Forming an equation means turning words into algebra.
Definition: An equation is formed by writing two equal expressions from the information given.
If a number plus 5 is 18, write .
Meaning: Age problems compare ages at different times.
Definition: An age problem uses relationships between present, past, or future ages.
If present age is x, age after 5 years is and age 3 years ago is .
Meaning: Digit problems use place value.
Definition: A twigit number with tens digit a and ones digit b is 10.
If tens digit is x and ones digit is 4, the number is 10.
Meaning: Perimeter problems use boundary formulas.
Definition: A perimeter equation is formed by setting the perimeter formula equal to the given perimeter.
For a rectangle, 2iven perimeter.
Easy
Question: A number increased by 9 is 24. Find the number.
Medium
Question: Ravi is x years old. After 6 years, he will be 20. Find his present age.
Exam-level
Question: The length of a rectangle is 3 cm more than its breadth. Its perimeter is 34 cm. Find its breadth.
Choosing a variable but not defining it
Why it happens: The equation is started too quickly.
Correct approach: Write what x represents before forming the equation.
Writing a twigit number as
Why it happens: Place value is forgotten.
Correct approach: Use 10.
Adding years for past age
Why it happens: Time direction is not checked.
Correct approach: Future adds years. Past subtracts years.
Using area instead of perimeter
Why it happens: The shape formula is chosen by habit.
Correct approach: Read whether the question asks for boundary or surface.
What is the hardest part of word problems?
Usually it is forming the equation, not solving it.
Why is a twigit number 10?
The tens digit is worth ten times its value, and the ones digit is added.
Should I check the answer in the sentence?
Yes. The final value should make sense in the original situation.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.