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Finding the Third Proportional to 284,764 and 412,457

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Solution

The third proportional to 284,764 and 412,457 is: 597,409.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    284,764 : 412,457 = 412,457 : x
  2. Step 2: Convert to fraction form
    284,764/412,457 = 412,457/x
  3. Step 3: Cross multiply
    284,764x = 412,457 × 412,457
  4. Step 4: Simplify right side
    284,764x = 170,120,776,849
  5. Step 5: Solve for x
    x = 170,120,776,849/284,764
  6. Step 6: Final answer
    x = 597,409.70

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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.