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Finding the Third Proportional to 81,824 and 172,396

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Solution

The third proportional to 81,824 and 172,396 is: 363,223.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,824 : 172,396 = 172,396 : x
  2. Step 2: Convert to fraction form
    81,824/172,396 = 172,396/x
  3. Step 3: Cross multiply
    81,824x = 172,396 × 172,396
  4. Step 4: Simplify right side
    81,824x = 29,720,380,816
  5. Step 5: Solve for x
    x = 29,720,380,816/81,824
  6. Step 6: Final answer
    x = 363,223.27

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.