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Finding the Third Proportional to 322,058 and 464,511

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Solution

The third proportional to 322,058 and 464,511 is: 669,973.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    322,058 : 464,511 = 464,511 : x
  2. Step 2: Convert to fraction form
    322,058/464,511 = 464,511/x
  3. Step 3: Cross multiply
    322,058x = 464,511 × 464,511
  4. Step 4: Simplify right side
    322,058x = 215,770,469,121
  5. Step 5: Solve for x
    x = 215,770,469,121/322,058
  6. Step 6: Final answer
    x = 669,973.95

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.