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Finding the Third Proportional to 284,564 and 412,156

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Solution

The third proportional to 284,564 and 412,156 is: 596,957.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    284,564 : 412,156 = 412,156 : x
  2. Step 2: Convert to fraction form
    284,564/412,156 = 412,156/x
  3. Step 3: Cross multiply
    284,564x = 412,156 × 412,156
  4. Step 4: Simplify right side
    284,564x = 169,872,568,336
  5. Step 5: Solve for x
    x = 169,872,568,336/284,564
  6. Step 6: Final answer
    x = 596,957.34

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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.