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Finding the Third Proportional to 102,469 and 210,041

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Solution

The third proportional to 102,469 and 210,041 is: 430,542.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,469 : 210,041 = 210,041 : x
  2. Step 2: Convert to fraction form
    102,469/210,041 = 210,041/x
  3. Step 3: Cross multiply
    102,469x = 210,041 × 210,041
  4. Step 4: Simplify right side
    102,469x = 44,117,221,681
  5. Step 5: Solve for x
    x = 44,117,221,681/102,469
  6. Step 6: Final answer
    x = 430,542.13

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.