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Finding the Third Proportional to 781 and 1,698

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Solution

The third proportional to 781 and 1,698 is: 3,691.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    781 : 1,698 = 1,698 : x
  2. Step 2: Convert to fraction form
    781/1,698 = 1,698/x
  3. Step 3: Cross multiply
    781x = 1,698 × 1,698
  4. Step 4: Simplify right side
    781x = 2,883,204
  5. Step 5: Solve for x
    x = 2,883,204/781
  6. Step 6: Final answer
    x = 3,691.68

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.