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Finding the Third Proportional to 205,614 and 458,506

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Solution

The third proportional to 205,614 and 458,506 is: 1,022,438.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,614 : 458,506 = 458,506 : x
  2. Step 2: Convert to fraction form
    205,614/458,506 = 458,506/x
  3. Step 3: Cross multiply
    205,614x = 458,506 × 458,506
  4. Step 4: Simplify right side
    205,614x = 210,227,752,036
  5. Step 5: Solve for x
    x = 210,227,752,036/205,614
  6. Step 6: Final answer
    x = 1,022,438.90

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.