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Finding the Third Proportional to 100,414 and 214,172

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Solution

The third proportional to 100,414 and 214,172 is: 456,805.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,414 : 214,172 = 214,172 : x
  2. Step 2: Convert to fraction form
    100,414/214,172 = 214,172/x
  3. Step 3: Cross multiply
    100,414x = 214,172 × 214,172
  4. Step 4: Simplify right side
    100,414x = 45,869,645,584
  5. Step 5: Solve for x
    x = 45,869,645,584/100,414
  6. Step 6: Final answer
    x = 456,805.28

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.