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Finding the Third Proportional to 103,834 and 218,036

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Solution

The third proportional to 103,834 and 218,036 is: 457,843.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    103,834 : 218,036 = 218,036 : x
  2. Step 2: Convert to fraction form
    103,834/218,036 = 218,036/x
  3. Step 3: Cross multiply
    103,834x = 218,036 × 218,036
  4. Step 4: Simplify right side
    103,834x = 47,539,697,296
  5. Step 5: Solve for x
    x = 47,539,697,296/103,834
  6. Step 6: Final answer
    x = 457,843.26

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.