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Finding the Third Proportional to 52,001 and 106,465

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Solution

The third proportional to 52,001 and 106,465 is: 217,972.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    52,001 : 106,465 = 106,465 : x
  2. Step 2: Convert to fraction form
    52,001/106,465 = 106,465/x
  3. Step 3: Cross multiply
    52,001x = 106,465 × 106,465
  4. Step 4: Simplify right side
    52,001x = 11,334,796,225
  5. Step 5: Solve for x
    x = 11,334,796,225/52,001
  6. Step 6: Final answer
    x = 217,972.66

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.