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Finding the Third Proportional to 409,658 and 596,475

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Solution

The third proportional to 409,658 and 596,475 is: 868,486.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    409,658 : 596,475 = 596,475 : x
  2. Step 2: Convert to fraction form
    409,658/596,475 = 596,475/x
  3. Step 3: Cross multiply
    409,658x = 596,475 × 596,475
  4. Step 4: Simplify right side
    409,658x = 355,782,425,625
  5. Step 5: Solve for x
    x = 355,782,425,625/409,658
  6. Step 6: Final answer
    x = 868,486.46

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.