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Finding the Third Proportional to 289 and 686

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Solution

The third proportional to 289 and 686 is: 1,628.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    289 : 686 = 686 : x
  2. Step 2: Convert to fraction form
    289/686 = 686/x
  3. Step 3: Cross multiply
    289x = 686 × 686
  4. Step 4: Simplify right side
    289x = 470,596
  5. Step 5: Solve for x
    x = 470,596/289
  6. Step 6: Final answer
    x = 1,628.36

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.