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Finding the Third Proportional to 29,691 and 65,214

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Solution

The third proportional to 29,691 and 65,214 is: 143,237.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    29,691 : 65,214 = 65,214 : x
  2. Step 2: Convert to fraction form
    29,691/65,214 = 65,214/x
  3. Step 3: Cross multiply
    29,691x = 65,214 × 65,214
  4. Step 4: Simplify right side
    29,691x = 4,252,865,796
  5. Step 5: Solve for x
    x = 4,252,865,796/29,691
  6. Step 6: Final answer
    x = 143,237.54

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.