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Finding the Third Proportional to 405,884 and 646,414

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Solution

The third proportional to 405,884 and 646,414 is: 1,029,483.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    405,884 : 646,414 = 646,414 : x
  2. Step 2: Convert to fraction form
    405,884/646,414 = 646,414/x
  3. Step 3: Cross multiply
    405,884x = 646,414 × 646,414
  4. Step 4: Simplify right side
    405,884x = 417,851,059,396
  5. Step 5: Solve for x
    x = 417,851,059,396/405,884
  6. Step 6: Final answer
    x = 1,029,483.94

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.