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Finding the Third Proportional to 102,423 and 214,494

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Solution

The third proportional to 102,423 and 214,494 is: 449,192.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,423 : 214,494 = 214,494 : x
  2. Step 2: Convert to fraction form
    102,423/214,494 = 214,494/x
  3. Step 3: Cross multiply
    102,423x = 214,494 × 214,494
  4. Step 4: Simplify right side
    102,423x = 46,007,676,036
  5. Step 5: Solve for x
    x = 46,007,676,036/102,423
  6. Step 6: Final answer
    x = 449,192.82

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.