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Finding the Third Proportional to 33,406 and 77,683

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Solution

The third proportional to 33,406 and 77,683 is: 180,645.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    33,406 : 77,683 = 77,683 : x
  2. Step 2: Convert to fraction form
    33,406/77,683 = 77,683/x
  3. Step 3: Cross multiply
    33,406x = 77,683 × 77,683
  4. Step 4: Simplify right side
    33,406x = 6,034,648,489
  5. Step 5: Solve for x
    x = 6,034,648,489/33,406
  6. Step 6: Final answer
    x = 180,645.65

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.