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Finding the Third Proportional to 686 and 1,463

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Solution

The third proportional to 686 and 1,463 is: 3,120.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    686 : 1,463 = 1,463 : x
  2. Step 2: Convert to fraction form
    686/1,463 = 1,463/x
  3. Step 3: Cross multiply
    686x = 1,463 × 1,463
  4. Step 4: Simplify right side
    686x = 2,140,369
  5. Step 5: Solve for x
    x = 2,140,369/686
  6. Step 6: Final answer
    x = 3,120.07

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.