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Finding the Third Proportional to 51,997 and 106,457

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Solution

The third proportional to 51,997 and 106,457 is: 217,956.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,997 : 106,457 = 106,457 : x
  2. Step 2: Convert to fraction form
    51,997/106,457 = 106,457/x
  3. Step 3: Cross multiply
    51,997x = 106,457 × 106,457
  4. Step 4: Simplify right side
    51,997x = 11,333,092,849
  5. Step 5: Solve for x
    x = 11,333,092,849/51,997
  6. Step 6: Final answer
    x = 217,956.67

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.