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Finding the Third Proportional to 6,413 and 13,814

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Solution

The third proportional to 6,413 and 13,814 is: 29,756.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,413 : 13,814 = 13,814 : x
  2. Step 2: Convert to fraction form
    6,413/13,814 = 13,814/x
  3. Step 3: Cross multiply
    6,413x = 13,814 × 13,814
  4. Step 4: Simplify right side
    6,413x = 190,826,596
  5. Step 5: Solve for x
    x = 190,826,596/6,413
  6. Step 6: Final answer
    x = 29,756.21

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.