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Finding the Third Proportional to 2,009 and 4,142

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Solution

The third proportional to 2,009 and 4,142 is: 8,539.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,009 : 4,142 = 4,142 : x
  2. Step 2: Convert to fraction form
    2,009/4,142 = 4,142/x
  3. Step 3: Cross multiply
    2,009x = 4,142 × 4,142
  4. Step 4: Simplify right side
    2,009x = 17,156,164
  5. Step 5: Solve for x
    x = 17,156,164/2,009
  6. Step 6: Final answer
    x = 8,539.65

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.