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Finding the Third Proportional to 102,966 and 164,441

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Solution

The third proportional to 102,966 and 164,441 is: 262,619.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,966 : 164,441 = 164,441 : x
  2. Step 2: Convert to fraction form
    102,966/164,441 = 164,441/x
  3. Step 3: Cross multiply
    102,966x = 164,441 × 164,441
  4. Step 4: Simplify right side
    102,966x = 27,040,842,481
  5. Step 5: Solve for x
    x = 27,040,842,481/102,966
  6. Step 6: Final answer
    x = 262,619.14

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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.