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Finding the Third Proportional to 49,704 and 106,823

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Solution

The third proportional to 49,704 and 106,823 is: 229,582.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,704 : 106,823 = 106,823 : x
  2. Step 2: Convert to fraction form
    49,704/106,823 = 106,823/x
  3. Step 3: Cross multiply
    49,704x = 106,823 × 106,823
  4. Step 4: Simplify right side
    49,704x = 11,411,153,329
  5. Step 5: Solve for x
    x = 11,411,153,329/49,704
  6. Step 6: Final answer
    x = 229,582.19

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.