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Finding the Third Proportional to 32,771 and 77,031

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Solution

The third proportional to 32,771 and 77,031 is: 181,067.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,771 : 77,031 = 77,031 : x
  2. Step 2: Convert to fraction form
    32,771/77,031 = 77,031/x
  3. Step 3: Cross multiply
    32,771x = 77,031 × 77,031
  4. Step 4: Simplify right side
    32,771x = 5,933,774,961
  5. Step 5: Solve for x
    x = 5,933,774,961/32,771
  6. Step 6: Final answer
    x = 181,067.86

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.