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Finding the Third Proportional to 106,966 and 164,429

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Solution

The third proportional to 106,966 and 164,429 is: 252,761.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,966 : 164,429 = 164,429 : x
  2. Step 2: Convert to fraction form
    106,966/164,429 = 164,429/x
  3. Step 3: Cross multiply
    106,966x = 164,429 × 164,429
  4. Step 4: Simplify right side
    106,966x = 27,036,896,041
  5. Step 5: Solve for x
    x = 27,036,896,041/106,966
  6. Step 6: Final answer
    x = 252,761.59

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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.