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Finding the Third Proportional to 181,408 and 397,824

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Solution

The third proportional to 181,408 and 397,824 is: 872,419.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    181,408 : 397,824 = 397,824 : x
  2. Step 2: Convert to fraction form
    181,408/397,824 = 397,824/x
  3. Step 3: Cross multiply
    181,408x = 397,824 × 397,824
  4. Step 4: Simplify right side
    181,408x = 158,263,934,976
  5. Step 5: Solve for x
    x = 158,263,934,976/181,408
  6. Step 6: Final answer
    x = 872,419.82

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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.