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Finding the Third Proportional to 414,084 and 582,966

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Solution

The third proportional to 414,084 and 582,966 is: 820,725.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,084 : 582,966 = 582,966 : x
  2. Step 2: Convert to fraction form
    414,084/582,966 = 582,966/x
  3. Step 3: Cross multiply
    414,084x = 582,966 × 582,966
  4. Step 4: Simplify right side
    414,084x = 339,849,357,156
  5. Step 5: Solve for x
    x = 339,849,357,156/414,084
  6. Step 6: Final answer
    x = 820,725.64

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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.