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Finding the Third Proportional to 105,866 and 164,102

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Solution

The third proportional to 105,866 and 164,102 is: 254,373.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,866 : 164,102 = 164,102 : x
  2. Step 2: Convert to fraction form
    105,866/164,102 = 164,102/x
  3. Step 3: Cross multiply
    105,866x = 164,102 × 164,102
  4. Step 4: Simplify right side
    105,866x = 26,929,466,404
  5. Step 5: Solve for x
    x = 26,929,466,404/105,866
  6. Step 6: Final answer
    x = 254,373.14

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.