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Finding the Third Proportional to 2,005 and 4,107.50

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Solution

The third proportional to 2,005 and 4,107.50 is: 8,414.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,005 : 4,107.50 = 4,107.50 : x
  2. Step 2: Convert to fraction form
    2,005/4,107.50 = 4,107.50/x
  3. Step 3: Cross multiply
    2,005x = 4,107.50 × 4,107.50
  4. Step 4: Simplify right side
    2,005x = 16,871,556.25
  5. Step 5: Solve for x
    x = 16,871,556.25/2,005
  6. Step 6: Final answer
    x = 8,414.74

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.