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Finding the Third Proportional to 5,766 and 6,414

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Solution

The third proportional to 5,766 and 6,414 is: 7,134.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,766 : 6,414 = 6,414 : x
  2. Step 2: Convert to fraction form
    5,766/6,414 = 6,414/x
  3. Step 3: Cross multiply
    5,766x = 6,414 × 6,414
  4. Step 4: Simplify right side
    5,766x = 41,139,396
  5. Step 5: Solve for x
    x = 41,139,396/5,766
  6. Step 6: Final answer
    x = 7,134.82

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.