Math Case Study for Class 8 on Linear Equation in One Variable

Class 8 Math Case Study on Linear Equations

A class 8 math case study on linear equations builds strong algebraic foundations. It helps students link mathematical expressions to real-world situations. Moreover, these math case study questions enhance logical reasoning and accuracy.

Why Linear Equations Matter in Mathematics

Understanding linear equations is essential for higher classes. It prepares students for Case Study math questions for class 9 and math case study questions class 9. Additionally, solving linear equation case studies improves analytical skills. Students can easily relate algebra to time, cost, and distance problems.

Practice for Better Results

To master math case study questions, learners should practice NCERT-based exercises regularly. Furthermore, interactive quizzes and worksheets make learning interesting. Hence, continuous practice of class 8 math case study linear equations ensures confidence during exams and strengthens problem-solving efficiency.

Case Study 1: Solving Real-life Problems using Linear Equations

Riya runs a small bakery that sells cupcakes and muffins. Each cupcake costs Rs. 25, and each muffin costs Rs. 30. One day, she sold a total of 40 items and collected Rs. 1100. After checking the record, she realized that she had sold more cupcakes than muffins. To understand her sales pattern, Riya decided to find out how many cupcakes and muffins she sold that day. She knows that by forming an equation based on the total number of items and total sales amount, she can easily find the quantities. This problem can be solved using the concept of linear equations in one variable, where we assume one quantity as \( x \) and form an equation in terms of \( x \).

Based on the above case study, answer the following questions:

1. If Riya sold \( x \) cupcakes, then how many muffins did she sell?
Solution:

Total items sold are 40. If \( x \) cupcakes are sold, remaining muffins \( = 40 – x \).

2. What is the correct linear equation representing the given situation?
Solution:

The total money earned = (Price of cupcakes × No. of cupcakes) + (Price of muffins × No. of muffins). Substituting gives \( 25x + 30(40 – x) = 1100 \).

3. What is the simplified form of the equation \( 25x + 30(40 – x) = 1100 \)?
Solution:

Expanding, \( 25x + 1200 – 30x = 1100 \). Simplify to \( -5x + 1200 = 1100 \).

4. What is the value of \( x \)?
Solution:

From \( -5x + 1200 = 1100 \), we get \( -5x = -100 \), hence \( x = 20 \).

5. How many muffins did Riya sell?
Solution:

Since \( x = 20 \) cupcakes, muffins = \( 40 – 20 = 20 \). Therefore, she sold 20 muffins.

Review your answers and solutions below:

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