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Finding the Third Proportional to 10,082 and 14,102

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Solution

The third proportional to 10,082 and 14,102 is: 19,724.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,082 : 14,102 = 14,102 : x
  2. Step 2: Convert to fraction form
    10,082/14,102 = 14,102/x
  3. Step 3: Cross multiply
    10,082x = 14,102 × 14,102
  4. Step 4: Simplify right side
    10,082x = 198,866,404
  5. Step 5: Solve for x
    x = 198,866,404/10,082
  6. Step 6: Final answer
    x = 19,724.90

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.