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Finding the Third Proportional to 2,005 and 2,305

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Solution

The third proportional to 2,005 and 2,305 is: 2,649.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,005 : 2,305 = 2,305 : x
  2. Step 2: Convert to fraction form
    2,005/2,305 = 2,305/x
  3. Step 3: Cross multiply
    2,005x = 2,305 × 2,305
  4. Step 4: Simplify right side
    2,005x = 5,313,025
  5. Step 5: Solve for x
    x = 5,313,025/2,005
  6. Step 6: Final answer
    x = 2,649.89

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.