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Finding the Third Proportional to 269,586 and 412,965

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Solution

The third proportional to 269,586 and 412,965 is: 632,599.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    269,586 : 412,965 = 412,965 : x
  2. Step 2: Convert to fraction form
    269,586/412,965 = 412,965/x
  3. Step 3: Cross multiply
    269,586x = 412,965 × 412,965
  4. Step 4: Simplify right side
    269,586x = 170,540,091,225
  5. Step 5: Solve for x
    x = 170,540,091,225/269,586
  6. Step 6: Final answer
    x = 632,599.95

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.