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Finding the Third Proportional to 997 and 1,269.50

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Solution

The third proportional to 997 and 1,269.50 is: 1,616.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    997 : 1,269.50 = 1,269.50 : x
  2. Step 2: Convert to fraction form
    997/1,269.50 = 1,269.50/x
  3. Step 3: Cross multiply
    997x = 1,269.50 × 1,269.50
  4. Step 4: Simplify right side
    997x = 1,611,630.25
  5. Step 5: Solve for x
    x = 1,611,630.25/997
  6. Step 6: Final answer
    x = 1,616.48

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.