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Finding the Third Proportional to 461,990 and 691,098

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Solution

The third proportional to 461,990 and 691,098 is: 1,033,824.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    461,990 : 691,098 = 691,098 : x
  2. Step 2: Convert to fraction form
    461,990/691,098 = 691,098/x
  3. Step 3: Cross multiply
    461,990x = 691,098 × 691,098
  4. Step 4: Simplify right side
    461,990x = 477,616,445,604
  5. Step 5: Solve for x
    x = 477,616,445,604/461,990
  6. Step 6: Final answer
    x = 1,033,824.21

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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.