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Finding the Third Proportional to 414,904 and 567,823

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Solution

The third proportional to 414,904 and 567,823 is: 777,102.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,904 : 567,823 = 567,823 : x
  2. Step 2: Convert to fraction form
    414,904/567,823 = 567,823/x
  3. Step 3: Cross multiply
    414,904x = 567,823 × 567,823
  4. Step 4: Simplify right side
    414,904x = 322,422,959,329
  5. Step 5: Solve for x
    x = 322,422,959,329/414,904
  6. Step 6: Final answer
    x = 777,102.56

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.