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Finding the Third Proportional to 198,047 and 412,413

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Solution

The third proportional to 198,047 and 412,413 is: 858,808.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,047 : 412,413 = 412,413 : x
  2. Step 2: Convert to fraction form
    198,047/412,413 = 412,413/x
  3. Step 3: Cross multiply
    198,047x = 412,413 × 412,413
  4. Step 4: Simplify right side
    198,047x = 170,084,482,569
  5. Step 5: Solve for x
    x = 170,084,482,569/198,047
  6. Step 6: Final answer
    x = 858,808.68

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.