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Finding the Third Proportional to 2,006 and 2,897

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Solution

The third proportional to 2,006 and 2,897 is: 4,183.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,006 : 2,897 = 2,897 : x
  2. Step 2: Convert to fraction form
    2,006/2,897 = 2,897/x
  3. Step 3: Cross multiply
    2,006x = 2,897 × 2,897
  4. Step 4: Simplify right side
    2,006x = 8,392,609
  5. Step 5: Solve for x
    x = 8,392,609/2,006
  6. Step 6: Final answer
    x = 4,183.75

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.