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Finding the Third Proportional to 6,537 and 13,497

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Solution

The third proportional to 6,537 and 13,497 is: 27,867.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,537 : 13,497 = 13,497 : x
  2. Step 2: Convert to fraction form
    6,537/13,497 = 13,497/x
  3. Step 3: Cross multiply
    6,537x = 13,497 × 13,497
  4. Step 4: Simplify right side
    6,537x = 182,169,009
  5. Step 5: Solve for x
    x = 182,169,009/6,537
  6. Step 6: Final answer
    x = 27,867.37

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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.