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Finding the Third Proportional to 512,867 and 691,659

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Solution

The third proportional to 512,867 and 691,659 is: 932,780.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    512,867 : 691,659 = 691,659 : x
  2. Step 2: Convert to fraction form
    512,867/691,659 = 691,659/x
  3. Step 3: Cross multiply
    512,867x = 691,659 × 691,659
  4. Step 4: Simplify right side
    512,867x = 478,392,172,281
  5. Step 5: Solve for x
    x = 478,392,172,281/512,867
  6. Step 6: Final answer
    x = 932,780.18

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.