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Finding the Third Proportional to 54,401 and 97,012

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Solution

The third proportional to 54,401 and 97,012 is: 172,999.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    54,401 : 97,012 = 97,012 : x
  2. Step 2: Convert to fraction form
    54,401/97,012 = 97,012/x
  3. Step 3: Cross multiply
    54,401x = 97,012 × 97,012
  4. Step 4: Simplify right side
    54,401x = 9,411,328,144
  5. Step 5: Solve for x
    x = 9,411,328,144/54,401
  6. Step 6: Final answer
    x = 172,999.18

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.