Math Case Study Questions for Class 8 on Linear Equations | Practice Set

Math Case Study Questions for Class 8 on Linear Equations

Math case study questions for class 8 on linear equations help students connect algebraic principles with real-life applications. These math case study questions build a strong foundation for solving equations involving one variable. Moreover, they improve logical and analytical thinking.

Importance of Practicing Linear Equations

Practicing linear equations case study questions enables students to understand formulas and algebraic relationships. It also prepares them for Case Study math questions for class 9 and math case study questions class 9. Additionally, solving such problems develops reasoning and accuracy.

Download and Practice

Students can download NCERT-based PDFs for regular practice. Furthermore, solving math case study questions daily enhances exam performance and strengthens conceptual understanding.

Case Study 3: Age Problem — Understanding Relationships through Linear Equations

Arjun and his father have a special relationship based on age differences. At present, Arjun’s father is three times as old as Arjun. After 5 years, the father’s age will be only twice that of Arjun. Both Arjun and his father are curious to know their current ages. Arjun decides to represent this real-life situation algebraically using a linear equation in one variable. He takes his present age as \( x \) years and forms an equation based on the given condition. Solving this equation will not only help determine their present ages but also explain how mathematical reasoning can simplify such daily life relationships. The problem involves careful transposition and balancing of terms on both sides to isolate the variable. It also reinforces the importance of interpreting results correctly within the context (i.e., ages must be positive integers).

1. If Arjun’s present age is \( x \) years, what will be his father’s present age?
Solution:

It is given that Arjun’s father is three times as old as Arjun, hence father’s age = \( 3x \).

2. After 5 years, what will be their respective ages?
Solution:

After 5 years, both ages increase by 5. Hence, Arjun’s age \( = x + 5 \), father’s age \( = 3x + 5 \).

3. According to the question, after 5 years, father’s age will be twice Arjun’s age. What equation can be formed?
Solution:

After 5 years, father’s age \( = 3x + 5 \) and Arjun’s age \( = x + 5 \). Given relation: father’s age \( = 2 \times \) (Arjun’s age).

4. Simplify the equation \( 3x + 5 = 2(x + 5) \) to find \( x \).
Solution:

Simplify \( 3x + 5 = 2x + 10 \). Subtract \( 2x \) and 5: \( x = 5 \). Hence, Arjun’s present age is 5 years.

5. What is Arjun’s father’s present age?
Solution:

Father’s age \( = 3x = 3 \times 5 = 15 \) years. Hence, Arjun is 5 years old and his father is 15 years old.

Review your answers and solutions below:

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