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Finding the Third Proportional to 8,192 and 17,698

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Solution

The third proportional to 8,192 and 17,698 is: 38,234.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,192 : 17,698 = 17,698 : x
  2. Step 2: Convert to fraction form
    8,192/17,698 = 17,698/x
  3. Step 3: Cross multiply
    8,192x = 17,698 × 17,698
  4. Step 4: Simplify right side
    8,192x = 313,219,204
  5. Step 5: Solve for x
    x = 313,219,204/8,192
  6. Step 6: Final answer
    x = 38,234.77

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.