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Finding the Third Proportional to 284,596 and 412,198

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Solution

The third proportional to 284,596 and 412,198 is: 597,011.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    284,596 : 412,198 = 412,198 : x
  2. Step 2: Convert to fraction form
    284,596/412,198 = 412,198/x
  3. Step 3: Cross multiply
    284,596x = 412,198 × 412,198
  4. Step 4: Simplify right side
    284,596x = 169,907,191,204
  5. Step 5: Solve for x
    x = 169,907,191,204/284,596
  6. Step 6: Final answer
    x = 597,011.87

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.