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Finding the Third Proportional to 11,497 and 23,731

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Solution

The third proportional to 11,497 and 23,731 is: 48,983.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    11,497 : 23,731 = 23,731 : x
  2. Step 2: Convert to fraction form
    11,497/23,731 = 23,731/x
  3. Step 3: Cross multiply
    11,497x = 23,731 × 23,731
  4. Step 4: Simplify right side
    11,497x = 563,160,361
  5. Step 5: Solve for x
    x = 563,160,361/11,497
  6. Step 6: Final answer
    x = 48,983.24

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.