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Finding the Third Proportional to 205.75 and 494.75

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Solution

The third proportional to 205.75 and 494.75 is: 1,189.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.75 : 494.75 = 494.75 : x
  2. Step 2: Convert to fraction form
    205.75/494.75 = 494.75/x
  3. Step 3: Cross multiply
    205.75x = 494.75 × 494.75
  4. Step 4: Simplify right side
    205.75x = 244,777.56
  5. Step 5: Solve for x
    x = 244,777.56/205.75
  6. Step 6: Final answer
    x = 1,189.68

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Why These Related Problems?

These problems maintain the same ratio (2.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.