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Finding the Third Proportional to 414,032 and 585,975

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Solution

The third proportional to 414,032 and 585,975 is: 829,324.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,032 : 585,975 = 585,975 : x
  2. Step 2: Convert to fraction form
    414,032/585,975 = 585,975/x
  3. Step 3: Cross multiply
    414,032x = 585,975 × 585,975
  4. Step 4: Simplify right side
    414,032x = 343,366,700,625
  5. Step 5: Solve for x
    x = 343,366,700,625/414,032
  6. Step 6: Final answer
    x = 829,324.06

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.