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Finding the Third Proportional to 9,864 and 14,049

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Solution

The third proportional to 9,864 and 14,049 is: 20,009.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,864 : 14,049 = 14,049 : x
  2. Step 2: Convert to fraction form
    9,864/14,049 = 14,049/x
  3. Step 3: Cross multiply
    9,864x = 14,049 × 14,049
  4. Step 4: Simplify right side
    9,864x = 197,374,401
  5. Step 5: Solve for x
    x = 197,374,401/9,864
  6. Step 6: Final answer
    x = 20,009.57

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.