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Finding the Third Proportional to 264,539 and 397,411

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Solution

The third proportional to 264,539 and 397,411 is: 597,021.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    264,539 : 397,411 = 397,411 : x
  2. Step 2: Convert to fraction form
    264,539/397,411 = 397,411/x
  3. Step 3: Cross multiply
    264,539x = 397,411 × 397,411
  4. Step 4: Simplify right side
    264,539x = 157,935,502,921
  5. Step 5: Solve for x
    x = 157,935,502,921/264,539
  6. Step 6: Final answer
    x = 597,021.62

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.