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Finding the Third Proportional to 214,784 and 464,966

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Solution

The third proportional to 214,784 and 464,966 is: 1,006,561.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,784 : 464,966 = 464,966 : x
  2. Step 2: Convert to fraction form
    214,784/464,966 = 464,966/x
  3. Step 3: Cross multiply
    214,784x = 464,966 × 464,966
  4. Step 4: Simplify right side
    214,784x = 216,193,381,156
  5. Step 5: Solve for x
    x = 216,193,381,156/214,784
  6. Step 6: Final answer
    x = 1,006,561.85

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.