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Finding the Third Proportional to 177,824 and 419,744

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Solution

The third proportional to 177,824 and 419,744 is: 990,783.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    177,824 : 419,744 = 419,744 : x
  2. Step 2: Convert to fraction form
    177,824/419,744 = 419,744/x
  3. Step 3: Cross multiply
    177,824x = 419,744 × 419,744
  4. Step 4: Simplify right side
    177,824x = 176,185,025,536
  5. Step 5: Solve for x
    x = 176,185,025,536/177,824
  6. Step 6: Final answer
    x = 990,783.17

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.