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Finding the Third Proportional to 502,024 and 764,801

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Solution

The third proportional to 502,024 and 764,801 is: 1,165,124.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    502,024 : 764,801 = 764,801 : x
  2. Step 2: Convert to fraction form
    502,024/764,801 = 764,801/x
  3. Step 3: Cross multiply
    502,024x = 764,801 × 764,801
  4. Step 4: Simplify right side
    502,024x = 584,920,569,601
  5. Step 5: Solve for x
    x = 584,920,569,601/502,024
  6. Step 6: Final answer
    x = 1,165,124.71

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.