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Finding the Third Proportional to 6,494 and 9,823

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Solution

The third proportional to 6,494 and 9,823 is: 14,858.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,494 : 9,823 = 9,823 : x
  2. Step 2: Convert to fraction form
    6,494/9,823 = 9,823/x
  3. Step 3: Cross multiply
    6,494x = 9,823 × 9,823
  4. Step 4: Simplify right side
    6,494x = 96,491,329
  5. Step 5: Solve for x
    x = 96,491,329/6,494
  6. Step 6: Final answer
    x = 14,858.54

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.