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Finding the Third Proportional to 10,823 and 16,234

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Solution

The third proportional to 10,823 and 16,234 is: 24,350.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,823 : 16,234 = 16,234 : x
  2. Step 2: Convert to fraction form
    10,823/16,234 = 16,234/x
  3. Step 3: Cross multiply
    10,823x = 16,234 × 16,234
  4. Step 4: Simplify right side
    10,823x = 263,542,756
  5. Step 5: Solve for x
    x = 263,542,756/10,823
  6. Step 6: Final answer
    x = 24,350.25

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.