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Finding the Third Proportional to 12,082 and 14,296

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Solution

The third proportional to 12,082 and 14,296 is: 16,915.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,082 : 14,296 = 14,296 : x
  2. Step 2: Convert to fraction form
    12,082/14,296 = 14,296/x
  3. Step 3: Cross multiply
    12,082x = 14,296 × 14,296
  4. Step 4: Simplify right side
    12,082x = 204,375,616
  5. Step 5: Solve for x
    x = 204,375,616/12,082
  6. Step 6: Final answer
    x = 16,915.71

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.