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Finding the Third Proportional to 32,006 and 68,098

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Solution

The third proportional to 32,006 and 68,098 is: 144,889.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,006 : 68,098 = 68,098 : x
  2. Step 2: Convert to fraction form
    32,006/68,098 = 68,098/x
  3. Step 3: Cross multiply
    32,006x = 68,098 × 68,098
  4. Step 4: Simplify right side
    32,006x = 4,637,337,604
  5. Step 5: Solve for x
    x = 4,637,337,604/32,006
  6. Step 6: Final answer
    x = 144,889.63

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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.