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Finding the Third Proportional to 384,177 and 563,809

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Solution

The third proportional to 384,177 and 563,809 is: 827,432.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    384,177 : 563,809 = 563,809 : x
  2. Step 2: Convert to fraction form
    384,177/563,809 = 563,809/x
  3. Step 3: Cross multiply
    384,177x = 563,809 × 563,809
  4. Step 4: Simplify right side
    384,177x = 317,880,588,481
  5. Step 5: Solve for x
    x = 317,880,588,481/384,177
  6. Step 6: Final answer
    x = 827,432.64

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.