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Finding the Third Proportional to 6,401 and 14,006

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Solution

The third proportional to 6,401 and 14,006 is: 30,646.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,401 : 14,006 = 14,006 : x
  2. Step 2: Convert to fraction form
    6,401/14,006 = 14,006/x
  3. Step 3: Cross multiply
    6,401x = 14,006 × 14,006
  4. Step 4: Simplify right side
    6,401x = 196,168,036
  5. Step 5: Solve for x
    x = 196,168,036/6,401
  6. Step 6: Final answer
    x = 30,646.47

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.