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Finding the Third Proportional to 512,411 and 729,941

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Solution

The third proportional to 512,411 and 729,941 is: 1,039,817.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    512,411 : 729,941 = 729,941 : x
  2. Step 2: Convert to fraction form
    512,411/729,941 = 729,941/x
  3. Step 3: Cross multiply
    512,411x = 729,941 × 729,941
  4. Step 4: Simplify right side
    512,411x = 532,813,863,481
  5. Step 5: Solve for x
    x = 532,813,863,481/512,411
  6. Step 6: Final answer
    x = 1,039,817.38

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.