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Finding the Third Proportional to 6,497 and 10,421

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Solution

The third proportional to 6,497 and 10,421 is: 16,714.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,497 : 10,421 = 10,421 : x
  2. Step 2: Convert to fraction form
    6,497/10,421 = 10,421/x
  3. Step 3: Cross multiply
    6,497x = 10,421 × 10,421
  4. Step 4: Simplify right side
    6,497x = 108,597,241
  5. Step 5: Solve for x
    x = 108,597,241/6,497
  6. Step 6: Final answer
    x = 16,714.98

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.