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Finding the Third Proportional to 4,027 and 6,407

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Solution

The third proportional to 4,027 and 6,407 is: 10,193.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,027 : 6,407 = 6,407 : x
  2. Step 2: Convert to fraction form
    4,027/6,407 = 6,407/x
  3. Step 3: Cross multiply
    4,027x = 6,407 × 6,407
  4. Step 4: Simplify right side
    4,027x = 41,049,649
  5. Step 5: Solve for x
    x = 41,049,649/4,027
  6. Step 6: Final answer
    x = 10,193.61

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.