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Finding the Third Proportional to 75,640 and 105,997

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Solution

The third proportional to 75,640 and 105,997 is: 148,537.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,640 : 105,997 = 105,997 : x
  2. Step 2: Convert to fraction form
    75,640/105,997 = 105,997/x
  3. Step 3: Cross multiply
    75,640x = 105,997 × 105,997
  4. Step 4: Simplify right side
    75,640x = 11,235,364,009
  5. Step 5: Solve for x
    x = 11,235,364,009/75,640
  6. Step 6: Final answer
    x = 148,537.33

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.