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Finding the Third Proportional to 686 and 1,029.75

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Solution

The third proportional to 686 and 1,029.75 is: 1,545.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    686 : 1,029.75 = 1,029.75 : x
  2. Step 2: Convert to fraction form
    686/1,029.75 = 1,029.75/x
  3. Step 3: Cross multiply
    686x = 1,029.75 × 1,029.75
  4. Step 4: Simplify right side
    686x = 1,060,385.06
  5. Step 5: Solve for x
    x = 1,060,385.06/686
  6. Step 6: Final answer
    x = 1,545.75

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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.