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Finding the Third Proportional to 461,580 and 698,517

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Solution

The third proportional to 461,580 and 698,517 is: 1,057,077.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    461,580 : 698,517 = 698,517 : x
  2. Step 2: Convert to fraction form
    461,580/698,517 = 698,517/x
  3. Step 3: Cross multiply
    461,580x = 698,517 × 698,517
  4. Step 4: Simplify right side
    461,580x = 487,925,999,289
  5. Step 5: Solve for x
    x = 487,925,999,289/461,580
  6. Step 6: Final answer
    x = 1,057,077.86

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.