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Finding the Third Proportional to 6,419 and 9,406

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Solution

The third proportional to 6,419 and 9,406 is: 13,782.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,419 : 9,406 = 9,406 : x
  2. Step 2: Convert to fraction form
    6,419/9,406 = 9,406/x
  3. Step 3: Cross multiply
    6,419x = 9,406 × 9,406
  4. Step 4: Simplify right side
    6,419x = 88,472,836
  5. Step 5: Solve for x
    x = 88,472,836/6,419
  6. Step 6: Final answer
    x = 13,782.96

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.