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Finding the Third Proportional to 412,993 and 581,593

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Solution

The third proportional to 412,993 and 581,593 is: 819,022.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,993 : 581,593 = 581,593 : x
  2. Step 2: Convert to fraction form
    412,993/581,593 = 581,593/x
  3. Step 3: Cross multiply
    412,993x = 581,593 × 581,593
  4. Step 4: Simplify right side
    412,993x = 338,250,417,649
  5. Step 5: Solve for x
    x = 338,250,417,649/412,993
  6. Step 6: Final answer
    x = 819,022.16

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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.