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Finding the Third Proportional to 102,821 and 219,214

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Solution

The third proportional to 102,821 and 219,214 is: 467,363.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,821 : 219,214 = 219,214 : x
  2. Step 2: Convert to fraction form
    102,821/219,214 = 219,214/x
  3. Step 3: Cross multiply
    102,821x = 219,214 × 219,214
  4. Step 4: Simplify right side
    102,821x = 48,054,777,796
  5. Step 5: Solve for x
    x = 48,054,777,796/102,821
  6. Step 6: Final answer
    x = 467,363.45

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.