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Finding the Third Proportional to 25,677 and 38,414

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Solution

The third proportional to 25,677 and 38,414 is: 57,469.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    25,677 : 38,414 = 38,414 : x
  2. Step 2: Convert to fraction form
    25,677/38,414 = 38,414/x
  3. Step 3: Cross multiply
    25,677x = 38,414 × 38,414
  4. Step 4: Simplify right side
    25,677x = 1,475,635,396
  5. Step 5: Solve for x
    x = 1,475,635,396/25,677
  6. Step 6: Final answer
    x = 57,469.15

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.