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Finding the Third Proportional to 6,814 and 14,357

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Solution

The third proportional to 6,814 and 14,357 is: 30,249.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,814 : 14,357 = 14,357 : x
  2. Step 2: Convert to fraction form
    6,814/14,357 = 14,357/x
  3. Step 3: Cross multiply
    6,814x = 14,357 × 14,357
  4. Step 4: Simplify right side
    6,814x = 206,123,449
  5. Step 5: Solve for x
    x = 206,123,449/6,814
  6. Step 6: Final answer
    x = 30,249.99

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.