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Finding the Third Proportional to 3,827 and 8,407

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Solution

The third proportional to 3,827 and 8,407 is: 18,468.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,827 : 8,407 = 8,407 : x
  2. Step 2: Convert to fraction form
    3,827/8,407 = 8,407/x
  3. Step 3: Cross multiply
    3,827x = 8,407 × 8,407
  4. Step 4: Simplify right side
    3,827x = 70,677,649
  5. Step 5: Solve for x
    x = 70,677,649/3,827
  6. Step 6: Final answer
    x = 18,468.16

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.