Susan had an incredible streak of good fortune as a guest on an exciting game show called “The Math Is Right.” She amassed winnings of $12,500, a sports car, two round-trip airline tickets, and five pieces of furniture

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. In an amazing finish, Susan then landed on a “Double Your Prize” square and answered the corresponding math question correctly. She instantly became the show’s biggest winner ever, earning twice the amounts of all her previous prizes. A week later, $25,000, a sports car, four round-trip airline tickets, and five pieces of furniture arrived at her house. Susan felt cheated. What was wrong?

Sangeetha Pulapaka

Step 1: Write a standard linear equation

             Recall the standard linear equation is of the form a x + by = c

             Let x be the airline tickets and y be the pieces of furniture and c be the total  


             So 2 x + 5 y = 12500

Step 2: Double the above linear equation

            Since Susan earned twice the amount

             ( 2 x + 5 y = 12500) \times 2

            4 x + 10 y =  25000

Step 3: Compare the two linear equations

            She should have received two sports cars and ten pieces of furniture

No wonder she felt cheated!