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Finding the Third Proportional to 81,784 and 119,983

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Solution

The third proportional to 81,784 and 119,983 is: 176,023.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,784 : 119,983 = 119,983 : x
  2. Step 2: Convert to fraction form
    81,784/119,983 = 119,983/x
  3. Step 3: Cross multiply
    81,784x = 119,983 × 119,983
  4. Step 4: Simplify right side
    81,784x = 14,395,920,289
  5. Step 5: Solve for x
    x = 14,395,920,289/81,784
  6. Step 6: Final answer
    x = 176,023.68

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.