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Finding the Third Proportional to 686 and 1,863

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Solution

The third proportional to 686 and 1,863 is: 5,059.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    686 : 1,863 = 1,863 : x
  2. Step 2: Convert to fraction form
    686/1,863 = 1,863/x
  3. Step 3: Cross multiply
    686x = 1,863 × 1,863
  4. Step 4: Simplify right side
    686x = 3,470,769
  5. Step 5: Solve for x
    x = 3,470,769/686
  6. Step 6: Final answer
    x = 5,059.43

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Why These Related Problems?

These problems maintain the same ratio (2.72) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.