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Finding the Third Proportional to 414,024 and 585,963

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Solution

The third proportional to 414,024 and 585,963 is: 829,306.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,024 : 585,963 = 585,963 : x
  2. Step 2: Convert to fraction form
    414,024/585,963 = 585,963/x
  3. Step 3: Cross multiply
    414,024x = 585,963 × 585,963
  4. Step 4: Simplify right side
    414,024x = 343,352,637,369
  5. Step 5: Solve for x
    x = 343,352,637,369/414,024
  6. Step 6: Final answer
    x = 829,306.12

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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.