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Finding the Third Proportional to 102,384 and 217,872

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Solution

The third proportional to 102,384 and 217,872 is: 463,629.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,384 : 217,872 = 217,872 : x
  2. Step 2: Convert to fraction form
    102,384/217,872 = 217,872/x
  3. Step 3: Cross multiply
    102,384x = 217,872 × 217,872
  4. Step 4: Simplify right side
    102,384x = 47,468,208,384
  5. Step 5: Solve for x
    x = 47,468,208,384/102,384
  6. Step 6: Final answer
    x = 463,629.16

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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.