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Finding the Third Proportional to 39,669 and 84,042

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Solution

The third proportional to 39,669 and 84,042 is: 178,049.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    39,669 : 84,042 = 84,042 : x
  2. Step 2: Convert to fraction form
    39,669/84,042 = 84,042/x
  3. Step 3: Cross multiply
    39,669x = 84,042 × 84,042
  4. Step 4: Simplify right side
    39,669x = 7,063,057,764
  5. Step 5: Solve for x
    x = 7,063,057,764/39,669
  6. Step 6: Final answer
    x = 178,049.81

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.