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Finding the Third Proportional to 1,109 and 2,047

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Solution

The third proportional to 1,109 and 2,047 is: 3,778.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,109 : 2,047 = 2,047 : x
  2. Step 2: Convert to fraction form
    1,109/2,047 = 2,047/x
  3. Step 3: Cross multiply
    1,109x = 2,047 × 2,047
  4. Step 4: Simplify right side
    1,109x = 4,190,209
  5. Step 5: Solve for x
    x = 4,190,209/1,109
  6. Step 6: Final answer
    x = 3,778.37

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Why These Related Problems?

These problems maintain the same ratio (1.85) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.