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Finding the Third Proportional to 12,416 and 16,864

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Solution

The third proportional to 12,416 and 16,864 is: 22,905.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,416 : 16,864 = 16,864 : x
  2. Step 2: Convert to fraction form
    12,416/16,864 = 16,864/x
  3. Step 3: Cross multiply
    12,416x = 16,864 × 16,864
  4. Step 4: Simplify right side
    12,416x = 284,394,496
  5. Step 5: Solve for x
    x = 284,394,496/12,416
  6. Step 6: Final answer
    x = 22,905.48

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.