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Finding the Third Proportional to 686 and 1,429

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Solution

The third proportional to 686 and 1,429 is: 2,976.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    686 : 1,429 = 1,429 : x
  2. Step 2: Convert to fraction form
    686/1,429 = 1,429/x
  3. Step 3: Cross multiply
    686x = 1,429 × 1,429
  4. Step 4: Simplify right side
    686x = 2,042,041
  5. Step 5: Solve for x
    x = 2,042,041/686
  6. Step 6: Final answer
    x = 2,976.74

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.