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Finding the Third Proportional to 6,569 and 14,191

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Solution

The third proportional to 6,569 and 14,191 is: 30,656.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,569 : 14,191 = 14,191 : x
  2. Step 2: Convert to fraction form
    6,569/14,191 = 14,191/x
  3. Step 3: Cross multiply
    6,569x = 14,191 × 14,191
  4. Step 4: Simplify right side
    6,569x = 201,384,481
  5. Step 5: Solve for x
    x = 201,384,481/6,569
  6. Step 6: Final answer
    x = 30,656.79

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.