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Finding the Third Proportional to 101,971 and 164,165

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Solution

The third proportional to 101,971 and 164,165 is: 264,292.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    101,971 : 164,165 = 164,165 : x
  2. Step 2: Convert to fraction form
    101,971/164,165 = 164,165/x
  3. Step 3: Cross multiply
    101,971x = 164,165 × 164,165
  4. Step 4: Simplify right side
    101,971x = 26,950,147,225
  5. Step 5: Solve for x
    x = 26,950,147,225/101,971
  6. Step 6: Final answer
    x = 264,292.27

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.