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Finding the Third Proportional to 284,642 and 412,275

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Solution

The third proportional to 284,642 and 412,275 is: 597,138.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    284,642 : 412,275 = 412,275 : x
  2. Step 2: Convert to fraction form
    284,642/412,275 = 412,275/x
  3. Step 3: Cross multiply
    284,642x = 412,275 × 412,275
  4. Step 4: Simplify right side
    284,642x = 169,970,675,625
  5. Step 5: Solve for x
    x = 169,970,675,625/284,642
  6. Step 6: Final answer
    x = 597,138.43

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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.