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Finding the Third Proportional to 81,784 and 182,128

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Solution

The third proportional to 81,784 and 182,128 is: 405,587.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,784 : 182,128 = 182,128 : x
  2. Step 2: Convert to fraction form
    81,784/182,128 = 182,128/x
  3. Step 3: Cross multiply
    81,784x = 182,128 × 182,128
  4. Step 4: Simplify right side
    81,784x = 33,170,608,384
  5. Step 5: Solve for x
    x = 33,170,608,384/81,784
  6. Step 6: Final answer
    x = 405,587.99

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.