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Finding the Third Proportional to 105,770 and 164,027

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Solution

The third proportional to 105,770 and 164,027 is: 254,371.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,770 : 164,027 = 164,027 : x
  2. Step 2: Convert to fraction form
    105,770/164,027 = 164,027/x
  3. Step 3: Cross multiply
    105,770x = 164,027 × 164,027
  4. Step 4: Simplify right side
    105,770x = 26,904,856,729
  5. Step 5: Solve for x
    x = 26,904,856,729/105,770
  6. Step 6: Final answer
    x = 254,371.34

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.