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Finding the Third Proportional to 102,321 and 209,561

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Solution

The third proportional to 102,321 and 209,561 is: 429,196.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,321 : 209,561 = 209,561 : x
  2. Step 2: Convert to fraction form
    102,321/209,561 = 209,561/x
  3. Step 3: Cross multiply
    102,321x = 209,561 × 209,561
  4. Step 4: Simplify right side
    102,321x = 43,915,812,721
  5. Step 5: Solve for x
    x = 43,915,812,721/102,321
  6. Step 6: Final answer
    x = 429,196.48

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.