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Finding the Third Proportional to 414,076 and 582,954

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Solution

The third proportional to 414,076 and 582,954 is: 820,707.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,076 : 582,954 = 582,954 : x
  2. Step 2: Convert to fraction form
    414,076/582,954 = 582,954/x
  3. Step 3: Cross multiply
    414,076x = 582,954 × 582,954
  4. Step 4: Simplify right side
    414,076x = 339,835,366,116
  5. Step 5: Solve for x
    x = 339,835,366,116/414,076
  6. Step 6: Final answer
    x = 820,707.71

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.