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Finding the Third Proportional to 31,782 and 68,519

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Solution

The third proportional to 31,782 and 68,519 is: 147,720.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,782 : 68,519 = 68,519 : x
  2. Step 2: Convert to fraction form
    31,782/68,519 = 68,519/x
  3. Step 3: Cross multiply
    31,782x = 68,519 × 68,519
  4. Step 4: Simplify right side
    31,782x = 4,694,853,361
  5. Step 5: Solve for x
    x = 4,694,853,361/31,782
  6. Step 6: Final answer
    x = 147,720.51

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.