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Finding the Third Proportional to 414,029 and 585,970

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Solution

The third proportional to 414,029 and 585,970 is: 829,315.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,029 : 585,970 = 585,970 : x
  2. Step 2: Convert to fraction form
    414,029/585,970 = 585,970/x
  3. Step 3: Cross multiply
    414,029x = 585,970 × 585,970
  4. Step 4: Simplify right side
    414,029x = 343,360,840,900
  5. Step 5: Solve for x
    x = 343,360,840,900/414,029
  6. Step 6: Final answer
    x = 829,315.92

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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.