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Finding the Third Proportional to 997 and 1,077

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Solution

The third proportional to 997 and 1,077 is: 1,163.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    997 : 1,077 = 1,077 : x
  2. Step 2: Convert to fraction form
    997/1,077 = 1,077/x
  3. Step 3: Cross multiply
    997x = 1,077 × 1,077
  4. Step 4: Simplify right side
    997x = 1,159,929
  5. Step 5: Solve for x
    x = 1,159,929/997
  6. Step 6: Final answer
    x = 1,163.42

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.