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Finding the Third Proportional to 856 and 1,997

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Solution

The third proportional to 856 and 1,997 is: 4,658.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    856 : 1,997 = 1,997 : x
  2. Step 2: Convert to fraction form
    856/1,997 = 1,997/x
  3. Step 3: Cross multiply
    856x = 1,997 × 1,997
  4. Step 4: Simplify right side
    856x = 3,988,009
  5. Step 5: Solve for x
    x = 3,988,009/856
  6. Step 6: Final answer
    x = 4,658.89

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.