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Finding the Third Proportional to 382,586 and 561,591

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Solution

The third proportional to 382,586 and 561,591 is: 824,349.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    382,586 : 561,591 = 561,591 : x
  2. Step 2: Convert to fraction form
    382,586/561,591 = 561,591/x
  3. Step 3: Cross multiply
    382,586x = 561,591 × 561,591
  4. Step 4: Simplify right side
    382,586x = 315,384,451,281
  5. Step 5: Solve for x
    x = 315,384,451,281/382,586
  6. Step 6: Final answer
    x = 824,349.17

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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.