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Finding the Third Proportional to 412,344 and 580,659

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Solution

The third proportional to 412,344 and 580,659 is: 817,678.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,344 : 580,659 = 580,659 : x
  2. Step 2: Convert to fraction form
    412,344/580,659 = 580,659/x
  3. Step 3: Cross multiply
    412,344x = 580,659 × 580,659
  4. Step 4: Simplify right side
    412,344x = 337,164,874,281
  5. Step 5: Solve for x
    x = 337,164,874,281/412,344
  6. Step 6: Final answer
    x = 817,678.62

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.