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Finding the Third Proportional to 9,705 and 20,517

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Solution

The third proportional to 9,705 and 20,517 is: 43,374.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,705 : 20,517 = 20,517 : x
  2. Step 2: Convert to fraction form
    9,705/20,517 = 20,517/x
  3. Step 3: Cross multiply
    9,705x = 20,517 × 20,517
  4. Step 4: Simplify right side
    9,705x = 420,947,289
  5. Step 5: Solve for x
    x = 420,947,289/9,705
  6. Step 6: Final answer
    x = 43,374.27

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.