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Finding the Third Proportional to 412,991 and 581,591

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Solution

The third proportional to 412,991 and 581,591 is: 819,020.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,991 : 581,591 = 581,591 : x
  2. Step 2: Convert to fraction form
    412,991/581,591 = 581,591/x
  3. Step 3: Cross multiply
    412,991x = 581,591 × 581,591
  4. Step 4: Simplify right side
    412,991x = 338,248,091,281
  5. Step 5: Solve for x
    x = 338,248,091,281/412,991
  6. Step 6: Final answer
    x = 819,020.49

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.