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Finding the Third Proportional to 39,857 and 83,782

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Solution

The third proportional to 39,857 and 83,782 is: 176,115.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    39,857 : 83,782 = 83,782 : x
  2. Step 2: Convert to fraction form
    39,857/83,782 = 83,782/x
  3. Step 3: Cross multiply
    39,857x = 83,782 × 83,782
  4. Step 4: Simplify right side
    39,857x = 7,019,423,524
  5. Step 5: Solve for x
    x = 7,019,423,524/39,857
  6. Step 6: Final answer
    x = 176,115.20

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.