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Finding the Third Proportional to 206,822 and 311,463

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Solution

The third proportional to 206,822 and 311,463 is: 469,046.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    206,822 : 311,463 = 311,463 : x
  2. Step 2: Convert to fraction form
    206,822/311,463 = 311,463/x
  3. Step 3: Cross multiply
    206,822x = 311,463 × 311,463
  4. Step 4: Simplify right side
    206,822x = 97,009,200,369
  5. Step 5: Solve for x
    x = 97,009,200,369/206,822
  6. Step 6: Final answer
    x = 469,046.81

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.