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Finding the Third Proportional to 31,412 and 68,006

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Solution

The third proportional to 31,412 and 68,006 is: 147,230.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,412 : 68,006 = 68,006 : x
  2. Step 2: Convert to fraction form
    31,412/68,006 = 68,006/x
  3. Step 3: Cross multiply
    31,412x = 68,006 × 68,006
  4. Step 4: Simplify right side
    31,412x = 4,624,816,036
  5. Step 5: Solve for x
    x = 4,624,816,036/31,412
  6. Step 6: Final answer
    x = 147,230.87

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.