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Finding the Third Proportional to 12,782 and 27,997

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Solution

The third proportional to 12,782 and 27,997 is: 61,323.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,782 : 27,997 = 27,997 : x
  2. Step 2: Convert to fraction form
    12,782/27,997 = 27,997/x
  3. Step 3: Cross multiply
    12,782x = 27,997 × 27,997
  4. Step 4: Simplify right side
    12,782x = 783,832,009
  5. Step 5: Solve for x
    x = 783,832,009/12,782
  6. Step 6: Final answer
    x = 61,323.11

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.