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Finding the Third Proportional to 461,916 and 691,011

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Solution

The third proportional to 461,916 and 691,011 is: 1,033,729.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    461,916 : 691,011 = 691,011 : x
  2. Step 2: Convert to fraction form
    461,916/691,011 = 691,011/x
  3. Step 3: Cross multiply
    461,916x = 691,011 × 691,011
  4. Step 4: Simplify right side
    461,916x = 477,496,202,121
  5. Step 5: Solve for x
    x = 477,496,202,121/461,916
  6. Step 6: Final answer
    x = 1,033,729.51

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.