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Finding the Third Proportional to 277,733 and 414,782

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Solution

The third proportional to 277,733 and 414,782 is: 619,458.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    277,733 : 414,782 = 414,782 : x
  2. Step 2: Convert to fraction form
    277,733/414,782 = 414,782/x
  3. Step 3: Cross multiply
    277,733x = 414,782 × 414,782
  4. Step 4: Simplify right side
    277,733x = 172,044,107,524
  5. Step 5: Solve for x
    x = 172,044,107,524/277,733
  6. Step 6: Final answer
    x = 619,458.64

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.