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Finding the Third Proportional to 321,856 and 685,292

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Solution

The third proportional to 321,856 and 685,292 is: 1,459,115.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    321,856 : 685,292 = 685,292 : x
  2. Step 2: Convert to fraction form
    321,856/685,292 = 685,292/x
  3. Step 3: Cross multiply
    321,856x = 685,292 × 685,292
  4. Step 4: Simplify right side
    321,856x = 469,625,125,264
  5. Step 5: Solve for x
    x = 469,625,125,264/321,856
  6. Step 6: Final answer
    x = 1,459,115.65

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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.