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Finding the Third Proportional to 177,822 and 419,747

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Solution

The third proportional to 177,822 and 419,747 is: 990,808.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    177,822 : 419,747 = 419,747 : x
  2. Step 2: Convert to fraction form
    177,822/419,747 = 419,747/x
  3. Step 3: Cross multiply
    177,822x = 419,747 × 419,747
  4. Step 4: Simplify right side
    177,822x = 176,187,544,009
  5. Step 5: Solve for x
    x = 176,187,544,009/177,822
  6. Step 6: Final answer
    x = 990,808.47

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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.