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Finding the Third Proportional to 106,462 and 230,456

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Solution

The third proportional to 106,462 and 230,456 is: 498,863.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,462 : 230,456 = 230,456 : x
  2. Step 2: Convert to fraction form
    106,462/230,456 = 230,456/x
  3. Step 3: Cross multiply
    106,462x = 230,456 × 230,456
  4. Step 4: Simplify right side
    106,462x = 53,109,967,936
  5. Step 5: Solve for x
    x = 53,109,967,936/106,462
  6. Step 6: Final answer
    x = 498,863.14

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.