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Finding the Third Proportional to 2,005 and 2,077

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Solution

The third proportional to 2,005 and 2,077 is: 2,151.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,005 : 2,077 = 2,077 : x
  2. Step 2: Convert to fraction form
    2,005/2,077 = 2,077/x
  3. Step 3: Cross multiply
    2,005x = 2,077 × 2,077
  4. Step 4: Simplify right side
    2,005x = 4,313,929
  5. Step 5: Solve for x
    x = 4,313,929/2,005
  6. Step 6: Final answer
    x = 2,151.59

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Why These Related Problems?

These problems maintain the same ratio (1.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.