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Finding the Third Proportional to 101,785 and 217,098

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Solution

The third proportional to 101,785 and 217,098 is: 463,049.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    101,785 : 217,098 = 217,098 : x
  2. Step 2: Convert to fraction form
    101,785/217,098 = 217,098/x
  3. Step 3: Cross multiply
    101,785x = 217,098 × 217,098
  4. Step 4: Simplify right side
    101,785x = 47,131,541,604
  5. Step 5: Solve for x
    x = 47,131,541,604/101,785
  6. Step 6: Final answer
    x = 463,049.97

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.