Linear Equations in One Variable Case Study Class 8 PDF Download

A mathematics club organized a competitive quiz and awarded a total cash prize of Rs. 960 to be shared among three winners: Asha, Bhavik and Chirag. The club announced that Asha should receive twice the amount Bhavik receives because Asha answered more high-value questions correctly. Additionally, Chirag is to receive one quarter of the combined amount received by Asha and Bhavik together, since he contributed in tie-break rounds. The organizers prefer to set up a single linear equation in one variable to determine each person’s share, using Bhavik’s share as the unknown. This case requires forming a precise linear equation from the word description, performing transposition and balancing to isolate the variable, checking that all shares are non-negative integers, and interpreting the result in context. Students must also verify the solution by summing the shares to confirm they equal the total prize. The problem illustrates how fractional relationships and proportional statements reduce to simple linear equations in one variable, and highlights the importance of correct arithmetic during simplification.