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Finding the Third Proportional to 12,206 and 19,469

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Solution

The third proportional to 12,206 and 19,469 is: 31,053.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,206 : 19,469 = 19,469 : x
  2. Step 2: Convert to fraction form
    12,206/19,469 = 19,469/x
  3. Step 3: Cross multiply
    12,206x = 19,469 × 19,469
  4. Step 4: Simplify right side
    12,206x = 379,041,961
  5. Step 5: Solve for x
    x = 379,041,961/12,206
  6. Step 6: Final answer
    x = 31,053.74

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.