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Finding the Third Proportional to 97,824 and 214,401

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Solution

The third proportional to 97,824 and 214,401 is: 469,902.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,824 : 214,401 = 214,401 : x
  2. Step 2: Convert to fraction form
    97,824/214,401 = 214,401/x
  3. Step 3: Cross multiply
    97,824x = 214,401 × 214,401
  4. Step 4: Simplify right side
    97,824x = 45,967,788,801
  5. Step 5: Solve for x
    x = 45,967,788,801/97,824
  6. Step 6: Final answer
    x = 469,902.98

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.