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Finding the Third Proportional to 2,049 and 2,209

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Solution

The third proportional to 2,049 and 2,209 is: 2,381.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,049 : 2,209 = 2,209 : x
  2. Step 2: Convert to fraction form
    2,049/2,209 = 2,209/x
  3. Step 3: Cross multiply
    2,049x = 2,209 × 2,209
  4. Step 4: Simplify right side
    2,049x = 4,879,681
  5. Step 5: Solve for x
    x = 4,879,681/2,049
  6. Step 6: Final answer
    x = 2,381.49

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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.