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Finding the Third Proportional to 4,214 and 6,497

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Solution

The third proportional to 4,214 and 6,497 is: 10,016.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,214 : 6,497 = 6,497 : x
  2. Step 2: Convert to fraction form
    4,214/6,497 = 6,497/x
  3. Step 3: Cross multiply
    4,214x = 6,497 × 6,497
  4. Step 4: Simplify right side
    4,214x = 42,211,009
  5. Step 5: Solve for x
    x = 42,211,009/4,214
  6. Step 6: Final answer
    x = 10,016.85

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.