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Finding the Third Proportional to 414,972 and 658,746

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Solution

The third proportional to 414,972 and 658,746 is: 1,045,724.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,972 : 658,746 = 658,746 : x
  2. Step 2: Convert to fraction form
    414,972/658,746 = 658,746/x
  3. Step 3: Cross multiply
    414,972x = 658,746 × 658,746
  4. Step 4: Simplify right side
    414,972x = 433,946,292,516
  5. Step 5: Solve for x
    x = 433,946,292,516/414,972
  6. Step 6: Final answer
    x = 1,045,724.27

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.