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Finding the Third Proportional to 410,414 and 616,809

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Solution

The third proportional to 410,414 and 616,809 is: 926,998.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    410,414 : 616,809 = 616,809 : x
  2. Step 2: Convert to fraction form
    410,414/616,809 = 616,809/x
  3. Step 3: Cross multiply
    410,414x = 616,809 × 616,809
  4. Step 4: Simplify right side
    410,414x = 380,453,342,481
  5. Step 5: Solve for x
    x = 380,453,342,481/410,414
  6. Step 6: Final answer
    x = 926,998.94

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.