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Finding the Third Proportional to 9,729 and 20,430

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Solution

The third proportional to 9,729 and 20,430 is: 42,901.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,729 : 20,430 = 20,430 : x
  2. Step 2: Convert to fraction form
    9,729/20,430 = 20,430/x
  3. Step 3: Cross multiply
    9,729x = 20,430 × 20,430
  4. Step 4: Simplify right side
    9,729x = 417,384,900
  5. Step 5: Solve for x
    x = 417,384,900/9,729
  6. Step 6: Final answer
    x = 42,901.11

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.