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Finding the Third Proportional to 205,776 and 309,212

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Solution

The third proportional to 205,776 and 309,212 is: 464,641.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,776 : 309,212 = 309,212 : x
  2. Step 2: Convert to fraction form
    205,776/309,212 = 309,212/x
  3. Step 3: Cross multiply
    205,776x = 309,212 × 309,212
  4. Step 4: Simplify right side
    205,776x = 95,612,060,944
  5. Step 5: Solve for x
    x = 95,612,060,944/205,776
  6. Step 6: Final answer
    x = 464,641.46

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.