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Finding the Third Proportional to 6,561 and 14,023

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Solution

The third proportional to 6,561 and 14,023 is: 29,971.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,561 : 14,023 = 14,023 : x
  2. Step 2: Convert to fraction form
    6,561/14,023 = 14,023/x
  3. Step 3: Cross multiply
    6,561x = 14,023 × 14,023
  4. Step 4: Simplify right side
    6,561x = 196,644,529
  5. Step 5: Solve for x
    x = 196,644,529/6,561
  6. Step 6: Final answer
    x = 29,971.73

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.