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Finding the Third Proportional to 414,161 and 566,746

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Solution

The third proportional to 414,161 and 566,746 is: 775,546.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,161 : 566,746 = 566,746 : x
  2. Step 2: Convert to fraction form
    414,161/566,746 = 566,746/x
  3. Step 3: Cross multiply
    414,161x = 566,746 × 566,746
  4. Step 4: Simplify right side
    414,161x = 321,201,028,516
  5. Step 5: Solve for x
    x = 321,201,028,516/414,161
  6. Step 6: Final answer
    x = 775,546.29

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.