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Finding the Third Proportional to 6,569 and 10,177

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Solution

The third proportional to 6,569 and 10,177 is: 15,766.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,569 : 10,177 = 10,177 : x
  2. Step 2: Convert to fraction form
    6,569/10,177 = 10,177/x
  3. Step 3: Cross multiply
    6,569x = 10,177 × 10,177
  4. Step 4: Simplify right side
    6,569x = 103,571,329
  5. Step 5: Solve for x
    x = 103,571,329/6,569
  6. Step 6: Final answer
    x = 15,766.68

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.