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Finding the Third Proportional to 1,102 and 2,049

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Solution

The third proportional to 1,102 and 2,049 is: 3,809.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102 : 2,049 = 2,049 : x
  2. Step 2: Convert to fraction form
    1,102/2,049 = 2,049/x
  3. Step 3: Cross multiply
    1,102x = 2,049 × 2,049
  4. Step 4: Simplify right side
    1,102x = 4,198,401
  5. Step 5: Solve for x
    x = 4,198,401/1,102
  6. Step 6: Final answer
    x = 3,809.80

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.