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Finding the Third Proportional to 769 and 1,397

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Solution

The third proportional to 769 and 1,397 is: 2,537.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    769 : 1,397 = 1,397 : x
  2. Step 2: Convert to fraction form
    769/1,397 = 1,397/x
  3. Step 3: Cross multiply
    769x = 1,397 × 1,397
  4. Step 4: Simplify right side
    769x = 1,951,609
  5. Step 5: Solve for x
    x = 1,951,609/769
  6. Step 6: Final answer
    x = 2,537.85

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Why These Related Problems?

These problems maintain the same ratio (1.82) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.