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Finding the Third Proportional to 6,412 and 9,749

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Solution

The third proportional to 6,412 and 9,749 is: 14,822.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,412 : 9,749 = 9,749 : x
  2. Step 2: Convert to fraction form
    6,412/9,749 = 9,749/x
  3. Step 3: Cross multiply
    6,412x = 9,749 × 9,749
  4. Step 4: Simplify right side
    6,412x = 95,043,001
  5. Step 5: Solve for x
    x = 95,043,001/6,412
  6. Step 6: Final answer
    x = 14,822.68

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.