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Finding the Third Proportional to 39,677 and 82,642

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Solution

The third proportional to 39,677 and 82,642 is: 172,132.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    39,677 : 82,642 = 82,642 : x
  2. Step 2: Convert to fraction form
    39,677/82,642 = 82,642/x
  3. Step 3: Cross multiply
    39,677x = 82,642 × 82,642
  4. Step 4: Simplify right side
    39,677x = 6,829,700,164
  5. Step 5: Solve for x
    x = 6,829,700,164/39,677
  6. Step 6: Final answer
    x = 172,132.47

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.