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Finding the Third Proportional to 409 and 698

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Solution

The third proportional to 409 and 698 is: 1,191.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 698 = 698 : x
  2. Step 2: Convert to fraction form
    409/698 = 698/x
  3. Step 3: Cross multiply
    409x = 698 × 698
  4. Step 4: Simplify right side
    409x = 487,204
  5. Step 5: Solve for x
    x = 487,204/409
  6. Step 6: Final answer
    x = 1,191.21

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Why These Related Problems?

These problems maintain the same ratio (1.71) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.