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Finding the Third Proportional to 414,396 and 584,919

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Solution

The third proportional to 414,396 and 584,919 is: 825,611.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,396 : 584,919 = 584,919 : x
  2. Step 2: Convert to fraction form
    414,396/584,919 = 584,919/x
  3. Step 3: Cross multiply
    414,396x = 584,919 × 584,919
  4. Step 4: Simplify right side
    414,396x = 342,130,236,561
  5. Step 5: Solve for x
    x = 342,130,236,561/414,396
  6. Step 6: Final answer
    x = 825,611.82

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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.