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Finding the Third Proportional to 106,198 and 165,749

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Solution

The third proportional to 106,198 and 165,749 is: 258,693.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,198 : 165,749 = 165,749 : x
  2. Step 2: Convert to fraction form
    106,198/165,749 = 165,749/x
  3. Step 3: Cross multiply
    106,198x = 165,749 × 165,749
  4. Step 4: Simplify right side
    106,198x = 27,472,731,001
  5. Step 5: Solve for x
    x = 27,472,731,001/106,198
  6. Step 6: Final answer
    x = 258,693.49

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.