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Finding the Third Proportional to 105,410 and 165,027

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Solution

The third proportional to 105,410 and 165,027 is: 258,361.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,410 : 165,027 = 165,027 : x
  2. Step 2: Convert to fraction form
    105,410/165,027 = 165,027/x
  3. Step 3: Cross multiply
    105,410x = 165,027 × 165,027
  4. Step 4: Simplify right side
    105,410x = 27,233,910,729
  5. Step 5: Solve for x
    x = 27,233,910,729/105,410
  6. Step 6: Final answer
    x = 258,361.74

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.