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Finding the Third Proportional to 102,441 and 217,302

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Solution

The third proportional to 102,441 and 217,302 is: 460,949.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,441 : 217,302 = 217,302 : x
  2. Step 2: Convert to fraction form
    102,441/217,302 = 217,302/x
  3. Step 3: Cross multiply
    102,441x = 217,302 × 217,302
  4. Step 4: Simplify right side
    102,441x = 47,220,159,204
  5. Step 5: Solve for x
    x = 47,220,159,204/102,441
  6. Step 6: Final answer
    x = 460,949.81

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.