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Finding the Third Proportional to 102,417 and 213,009

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Solution

The third proportional to 102,417 and 213,009 is: 443,020.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,417 : 213,009 = 213,009 : x
  2. Step 2: Convert to fraction form
    102,417/213,009 = 213,009/x
  3. Step 3: Cross multiply
    102,417x = 213,009 × 213,009
  4. Step 4: Simplify right side
    102,417x = 45,372,834,081
  5. Step 5: Solve for x
    x = 45,372,834,081/102,417
  6. Step 6: Final answer
    x = 443,020.53

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.