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Finding the Third Proportional to 20,011 and 31,414

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Solution

The third proportional to 20,011 and 31,414 is: 49,314.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    20,011 : 31,414 = 31,414 : x
  2. Step 2: Convert to fraction form
    20,011/31,414 = 31,414/x
  3. Step 3: Cross multiply
    20,011x = 31,414 × 31,414
  4. Step 4: Simplify right side
    20,011x = 986,839,396
  5. Step 5: Solve for x
    x = 986,839,396/20,011
  6. Step 6: Final answer
    x = 49,314.85

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.