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Finding the Third Proportional to 49,802 and 106,196

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Solution

The third proportional to 49,802 and 106,196 is: 226,448.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,802 : 106,196 = 106,196 : x
  2. Step 2: Convert to fraction form
    49,802/106,196 = 106,196/x
  3. Step 3: Cross multiply
    49,802x = 106,196 × 106,196
  4. Step 4: Simplify right side
    49,802x = 11,277,590,416
  5. Step 5: Solve for x
    x = 11,277,590,416/49,802
  6. Step 6: Final answer
    x = 226,448.54

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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.