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Finding the Third Proportional to 205,174 and 463,031

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Solution

The third proportional to 205,174 and 463,031 is: 1,044,955.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,174 : 463,031 = 463,031 : x
  2. Step 2: Convert to fraction form
    205,174/463,031 = 463,031/x
  3. Step 3: Cross multiply
    205,174x = 463,031 × 463,031
  4. Step 4: Simplify right side
    205,174x = 214,397,706,961
  5. Step 5: Solve for x
    x = 214,397,706,961/205,174
  6. Step 6: Final answer
    x = 1,044,955.54

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Why These Related Problems?

These problems maintain the same ratio (2.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.