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Finding the Third Proportional to 106,184 and 165,729

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Solution

The third proportional to 106,184 and 165,729 is: 258,665.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,184 : 165,729 = 165,729 : x
  2. Step 2: Convert to fraction form
    106,184/165,729 = 165,729/x
  3. Step 3: Cross multiply
    106,184x = 165,729 × 165,729
  4. Step 4: Simplify right side
    106,184x = 27,466,101,441
  5. Step 5: Solve for x
    x = 27,466,101,441/106,184
  6. Step 6: Final answer
    x = 258,665.16

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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.